Question

How to evaluate this sum $\sum_{n=0}^\infty \frac{\cos\left(\left(2n+1\right)\phi\right)}{\cos^{2n+1}\left(\phi\right)}$?

score 106 · Answer 1 · 2021-02-16 03:01:04

106

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How to evaluate this sum $\sum_{n=0}^\infty \frac{\cos\left(\left(2n+1\right)\phi\right)}{\cos^{2n+1}\left(\phi\right)}$?

Published on 16 Feb 2021 - 3:01

score 27 · Answer 2 · 2021-03-03 13:48:40

27

Views

Proof that if unordered sum is finite, then there are finitely many positive terms

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score 26 · Answer 3 · 2026-03-28 13:27:25

26

Views

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score 716 · Answer 4 · 2021-03-05 19:16:30

716

Views

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score 1.7k · Answer 5 · 2021-03-08 06:02:45

1.7k

Views

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score 41 · Answer 6 · 2021-03-08 18:09:18

41

Views

If Ratio Test for an alternating series is Divergent, Must I run the Alternating series test?

Published on 08 Mar 2021 - 18:09

score 173 · Answer 7 · 2021-03-09 13:45:47

173

Views

$x-\frac{1}{x} - \frac{1}{x-\frac{1}{x}} - \dots $ can we represent this infinite expression by an integral or a summation?

Published on 09 Mar 2021 - 13:45

score 69 · Answer 8 · 2021-03-09 19:42:50

69

Views

Partial sum of reciprocals of square roots of k-almost primes

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score 39 · Answer 9 · 2021-03-10 04:22:55

Given the power series, for all $c > 0 $ the power series either converges diverges or both, for at atleast one $x>0$, what is true?

score 135 · Answer 10 · 2021-03-11 01:50:31

135

Views

Simplify a log of a log and series

Published on 11 Mar 2021 - 1:50

score 125 · Answer 11 · 2021-03-22 00:05:45

125

Views

Is the series $ 1-1+1-1+1+\cdots = -1+1-1+1-1+1-\cdots $?

Published on 22 Mar 2021 - 0:05

score 696 · Answer 12 · 2021-03-22 01:50:08

696

Views

Suppose a series $a_n$ is greater than 0 for all positive integer n, and that $\sum \frac {a_n} n$ converges, then does the following also converge?

Published on 22 Mar 2021 - 1:50

score 49 · Answer 13 · 2021-03-25 02:54:17

49

Views

Convergence/Divergence of the series $\sum_{n=1}^{+\infty}(3^{1/n^2} -1) \csc^2n$

Published on 25 Mar 2021 - 2:54

score 275 · Answer 14 · 2026-02-23 16:55:55

275

Views

Why is $\ln 0\ne-\ln \infty$?

Published on 23 Feb 2026 - 16:55

score 78 · Answer 15 · 2026-03-26 14:43:03

78

Views

A converse to a lemma of Cesàro?

Published on 26 Mar 2026 - 14:43

List Question

How to evaluate this sum $\sum_{n=0}^\infty \frac{\cos\left(\left(2n+1\right)\phi\right)}{\cos^{2n+1}\left(\phi\right)}$?

Proof that if unordered sum is finite, then there are finitely many positive terms

Uniqueness of the Solution to a Difference Equation

Inconclusive convergence tests and Divergence Test

Achilles and the tortoise problem

If Ratio Test for an alternating series is Divergent, Must I run the Alternating series test?

$x-\frac{1}{x} - \frac{1}{x-\frac{1}{x}} - \dots $ can we represent this infinite expression by an integral or a summation?

Partial sum of reciprocals of square roots of k-almost primes

Given the power series, for all $c > 0 $ the power series either converges diverges or both, for at atleast one $x>0$, what is true?

Simplify a log of a log and series

Is the series $ 1-1+1-1+1+\cdots = -1+1-1+1-1+1-\cdots $?

Suppose a series $a_n$ is greater than 0 for all positive integer n, and that $\sum \frac {a_n} n$ converges, then does the following also converge?

Convergence/Divergence of the series $\sum_{n=1}^{+\infty}(3^{1/n^2} -1) \csc^2n$

Why is $\ln 0\ne-\ln \infty$?

A converse to a lemma of Cesàro?

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