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Find the $n^{th}$ term and the sum to $n$ terms of the series.

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#sequences-and-series #geometric-progressions
434
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On the series $\sum \limits_{n=1}^{\infty} \frac{\sin (n \pi y) \sin \left ( n \pi x \right )}{n^2 \pi^2}$

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#real-analysis #sequences-and-series #special-functions
242
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Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

Published on
#sequences-and-series #limits
55
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Finding limit of a convergent sequence

Published on
#sequences-and-series #limits #measure-theory #sequence-of-function
1.3k
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Benefit of studying series

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#calculus #real-analysis #sequences-and-series #number-theory #soft-question
74
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comparison of the limits of the expectations of two sequences of r.v.

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#probability #sequences-and-series #measure-theory #convergence-divergence
123
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Monty Hall Variant Game

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#probability #sequences-and-series #statistics #discrete-mathematics #monty-hall
86
Views

Show that sequence converges, hence find the limit.

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#integration #sequences-and-series #functional-analysis #proof-verification #lp-spaces
111
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Calculate the limit: $\lim\limits_{n\to\infty} a_n = \frac{1}{n^2}\sum\limits_{i=1}^ni\cdot e^\frac{i^2}{n^2}$

Published on
#sequences-and-series #limits
117
Views

Equivalence of definition of absolute convergence

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#sequences-and-series #convergence-divergence
78
Views

How to prove a series is convergent?

Published on
#calculus #sequences-and-series #proof-verification
111
Views

Writing sum as integral

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#sequences-and-series #improper-integrals
231
Views

How to find a constant that makes a geometric series convergent?

Published on
#calculus #sequences-and-series
264
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The integer part of $ \sum_{k=2}^{9999} \frac{1}{\sqrt{k}} $

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#sequences-and-series #inequality
2.5k
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Sub sub sequences and a relation between convergence in probability and a.s convergence

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#probability #sequences-and-series #convergence-divergence

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