https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/geometric-sequences-introduction 2024-03-31T16:17:16.747917574Z गुणोत्तर अनुक्रम का परिचय:भाग 1 (Intro to geometric sequences) Sal introduces geometric sequences and their main features, the initial term and the common ratio. Sal Khan video https://cdn.kastatic.org/googleusercontent/EGwJyoWiNK9S9o40xAqCEN70zhYCxmMpzmSCp5vp890CX6dQLAk-NetWrz9x17rxaUPCwwEGRpjxhQT_2WdqYjk गुणोत्तर अनुक्रम का परिचय:भाग 1 (Intro to geometric sequences) Sal introduces geometric sequences and their main features, the initial term and the common ratio. https://cdn.kastatic.org/ka-youtube-converted/bVPOp7p4gvs.mp4/bVPOp7p4gvs.mp4 645 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/worked-example-gp-formula-based 2025-03-24T05:52:22.847271672Z GP का उदाहरण (सूत्र पर आधारित) (Worked example GP (formula based)) Let's solve a worked example together which involves using the formula for GP. We're given the relation between two pairs of terms. Which means if we insert two variables in the system, we get figure them out using what we know. We assume the first term and the common ratio and follow along as the algebra guides the way! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw GP का उदाहरण (सूत्र पर आधारित) (Worked example GP (formula based)) Let's solve a worked example together which involves using the formula for GP. We're given the relation between two pairs of terms. Which means if we insert two variables in the system, we get figure them out using what we know. We assume the first term and the common ratio and follow along as the algebra guides the way! https://cdn.kastatic.org/ka-youtube-converted/wGNRWLRYYHM.mp4/wGNRWLRYYHM.mp4 242 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/formula-based-problems-gp 2025-06-25T04:36:24.163902917Z सूत्र आधारित समस्याएँ (GP) सूत्र आधारित समस्याएँ (GP) Ashish Gupta exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/worked-example-gp-proof-based 2025-03-24T05:52:22.847271672Z GP का उदाहरण (उपपत्ति पर आधारित) (Worked example GP (proof based)) Let's get rigorous and solve two proof based problems from the topic GP. The first one asks to figure out the ratio of sum of first n terms of a GP to the sum of next n terms. This problem teaches us how to move from 'what we know' to 'what we need'. The second problem asks us to figure out the product of first n terms. You read it right - not the sum, but the product. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw GP का उदाहरण (उपपत्ति पर आधारित) (Worked example GP (proof based)) Let's get rigorous and solve two proof based problems from the topic GP. The first one asks to figure out the ratio of sum of first n terms of a GP to the sum of next n terms. This problem teaches us how to move from 'what we know' to 'what we need'. The second problem asks us to figure out the product of first n terms. You read it right - not the sum, but the product. https://cdn.kastatic.org/ka-youtube-converted/ggV7HCJ6iDQ.mp4/ggV7HCJ6iDQ.mp4 450 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/worked-example-gp-challenge 2025-03-24T05:52:22.847271672Z GP: चुनौतीपूर्ण उदाहरण (Worked example GP challenge) What's 8 + 88 + 888 + 8888... ? How is this related to GP? Let's apply what we know about sequence and series to tackle this hairy looking problem. We can solve this problem directly. But we wont! We'll first observe the pattern to figure out the formula for the nth term of this sequence. We'll them break about the nth term and separately add back its components to figure out the sum of n terms. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw GP: चुनौतीपूर्ण उदाहरण (Worked example GP challenge) What's 8 + 88 + 888 + 8888... ? How is this related to GP? Let's apply what we know about sequence and series to tackle this hairy looking problem. We can solve this problem directly. But we wont! We'll first observe the pattern to figure out the formula for the nth term of this sequence. We'll them break about the nth term and separately add back its components to figure out the sum of n terms. https://cdn.kastatic.org/ka-youtube-converted/dhMH_WsHK18.mp4/dhMH_WsHK18.mp4 362 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/finding-terms-between-two-terms-of-a-gp 2025-03-24T05:52:22.847271672Z किसी एक GP के दो पदों के बीच पदों को ज्ञात करना (Finding terms between two terms of a GP) Given two terms, can we find more terms that lie between them that form a GP? Let's learn how to jump our way to solving such problems in this video. The key thing to realise is that we can actually ignore the missing terms for a while. All we need is the number of jumps. Finding the common ratio first simplifies the job for us. Using this approach we can figure out any number of terms between two given numbers. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw किसी एक GP के दो पदों के बीच पदों को ज्ञात करना (Finding terms between two terms of a GP) Given two terms, can we find more terms that lie between them that form a GP? Let's learn how to jump our way to solving such problems in this video. The key thing to realise is that we can actually ignore the missing terms for a while. All we need is the number of jumps. Finding the common ratio first simplifies the job for us. Using this approach we can figure out any number of terms between two given numbers. https://cdn.kastatic.org/ka-youtube-converted/eTmown9ktDU.mp4/eTmown9ktDU.mp4 266 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/geometric_sequences_1 2026-04-06T17:09:20.528545922Z गुणोत्तर अनुक्रमों का विस्तार करना गुणोत्तर अनुक्रम के पहले कुछ पद दिए होने पर, अनुक्रम का अगला पद ज्ञात कीजिए। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/geometric-sequences 2024-03-31T16:17:16.747917574Z गुणोत्तर अनुक्रम का परिचय(एडवांस्ड) (Intro to geometric sequences (advanced)) Sal introduces geometric sequences and gives a few examples. Notation used in this video is relatively advanced. Sal Khan video https://cdn.kastatic.org/googleusercontent/W9qzhM4EKA5aTH7RKXe-C1LbvwXtducqa6qbG7RRhZMLijoSeFPJczsw-H4eglFmCGA4zUOpEXwESCONZpzSkgeP गुणोत्तर अनुक्रम का परिचय(एडवांस्ड) (Intro to geometric sequences (advanced)) Sal introduces geometric sequences and gives a few examples. Notation used in this video is relatively advanced. https://cdn.kastatic.org/ka-youtube-converted/RopKLTlyAVk.mp4/RopKLTlyAVk.mp4 399 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/geometric_sequences_2 2025-03-24T05:52:22.847271672Z गुणोत्तर अनुक्रम सूत्रों का उपयोग करें किसी गुणोत्तर अनुक्रम का सूत्र दिया होने पर, चाहे वह सूत्र स्पष्ट (Explicit) रूप में हो या पुनरावर्ती (Recursive) रूप में, अनुक्रम का कोई विशिष्ट पद ज्ञात कीजिए। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/series-as-sum-of-sequence 2020-11-13T07:10:02Z गुणोत्तर श्रेणी परिचय (Geometric series intro) A geometric series is the sum of the terms of a geometric sequence. Learn more about it here. Sal Khan video https://cdn.kastatic.org/googleusercontent/TmSdYcKy73Yzh2Lwlb3RhiRliE_Ippk6x9DIoAtEk2197evzFXj08U7DSr91qZTj072cpqND7DIf_hRnrG9-NjwG गुणोत्तर श्रेणी परिचय (Geometric series intro) A geometric series is the sum of the terms of a geometric sequence. Learn more about it here. https://cdn.kastatic.org/ka-youtube-converted/DuR6bNbA-f8.mp4/DuR6bNbA-f8.mp4 173 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/deriving-formula-for-sum-of-finite-geometric-series 2025-01-02T14:29:17.724286289Z परिमित गुणोत्तर श्रेणी सूत्र (Finite geometric series formula) A finite geometric series can be solved using the formula a(1-rⁿ)/(1-r). Sal demonstrates how to derive a formula for the sum of the first 'n' terms of such a series, emphasizing the importance of understanding the number of terms being summed. video https://cdn.kastatic.org/ka_thumbnails_cache/d2be81fa-a733-4db8-8f50-05e253e9e679_1280_720_base.png परिमित गुणोत्तर श्रेणी सूत्र (Finite geometric series formula) A finite geometric series can be solved using the formula a(1-rⁿ)/(1-r). Sal demonstrates how to derive a formula for the sum of the first 'n' terms of such a series, emphasizing the importance of understanding the number of terms being summed. https://cdn.kastatic.org/ka-youtube-converted/Fsq8km1Pp00.mp4/Fsq8km1Pp00.mp4 435 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/example-finding-sum-of-finite-geometric-series 2025-01-02T14:29:17.724286289Z उदाहरण : परिमित गुणोत्तर श्रेणी (सिग्मा संकेत में ) (Worked example: finite geometric series (sigma notation)) Sal evaluates the geometric series Σ2(3ᵏ) for k=0 to 99 using the finite geometric series formula a(1-rⁿ)/(1-r). video https://cdn.kastatic.org/ka_thumbnails_cache/141f5f44-3e3e-41de-87b2-89e059c39be5_1280_720_base.png उदाहरण : परिमित गुणोत्तर श्रेणी (सिग्मा संकेत में ) (Worked example: finite geometric series (sigma notation)) Sal evaluates the geometric series Σ2(3ᵏ) for k=0 to 99 using the finite geometric series formula a(1-rⁿ)/(1-r). https://cdn.kastatic.org/ka-youtube-converted/4QbCecNWllM.mp4/4QbCecNWllM.mp4 168 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/geometric-series-formula 2025-03-24T05:52:22.847271672Z गुणोत्तर श्रेणी सूत्र अभ्यास करें कि आप गुणोत्तर श्रेणी सूत्र को कितना समझ सकें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/geometric-series--1 2025-03-24T05:52:22.847271672Z परिमित गुणोत्तर श्रेणी सिग्मा संकेत में, पुनरावर्ती रूप से या स्पष्ट रूप से दी गई परिमित गुणोत्तर श्रेणी की गणना करें। Tomer Gal exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/v/geometric-series-word-problem 2020-11-13T07:10:01Z परिमित गुणोत्तर श्रेणी शब्द समस्या: सोशल मीडिया (Finite geometric series word problem: social media) Watch Sal solve an example of using a geometric series to answer a fun word problem. Sal Khan video https://cdn.kastatic.org/googleusercontent/v392FVECsH38yNQR1hy859u7azBi8uS6CKMVJ46EXTVbf4IxS6Uqk6tB2q18Mi4GAjufHWcG7phlDJvsU-JSeohC8A परिमित गुणोत्तर श्रेणी शब्द समस्या: सोशल मीडिया (Finite geometric series word problem: social media) Watch Sal solve an example of using a geometric series to answer a fun word problem. https://cdn.kastatic.org/ka-youtube-converted/B4LxQtIXP3g.mp4/B4LxQtIXP3g.mp4 483 गुणोत्तर श्रेणी (Geometric progression) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:sequences-and-series-ncert-new/x808831787a7b08a2:geometric-progression/e/geometric-series 2025-03-27T03:46:46.605447955Z परिमित गुणोत्तर श्रेणी की शब्द समस्याएं परिमित ज्यामितीय श्रेणी के सूत्र के प्रश्नों को समझना तथा उनका हल निकालना Rhonda Hughes exercise