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Questions › JNU › JNU SIS 2019 › Q15
0 marksMathematics › Sequences, series and convergence › Convergence of seriesEasyabout 1 min

JNU SIS 2019 Question 15: Sequences, series and convergence

Let ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞​an​ be a convergent series and let S be its sum. Let Sn=∑i=1naiS_n = \sum_{i=1}^{n} a_iSn​=∑i=1n​ai​ be the n-th order partial sum. Then lim⁡n→∞Sn\lim_{n \to \infty} S_nlimn→∞​Sn​ and lim⁡n→∞an\lim_{n \to \infty} a_nlimn→∞​an​ are given by

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Let Σₙ₌₁^∞ aₙ be a convergent series and let S be its sum. Let Sₙ = Σᵢ₌₁ⁿ aᵢ be the n-th order partial sum. Then lim_(n → ∞) Sₙ and lim_(n → ∞) aₙ are given by (A) 1 and 0 respectively (B) 0 and 1 respectively (C) S and 0 respectively (D) S and 1 respectively

Also written as: Let sum_(n=1)^(inf) a_n be a convergent series and let S be its sum. Let S_n = sum_(i=1)^n a_i be the n-th order partial sum. Then lim_(n -> inf) S_n and lim_(n -> inf) a_n are given by

Sequences, series and convergence has come up 33 times in 5 exams since 2006.

What this question tests

This question is on Convergence of series, part of Sequences, series and convergence in Mathematics.

Tests for whether an infinite sum converges.

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Question from the JNU SIS 2019 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.