Question

The formula for the $n^\text{th}$ term of $\frac{x^2}6 -\frac{x^4}9 + \frac{3x^6}{80} - \frac{71 x^8}{15120} + \frac{ 10361 x^{10}}{10886400} \dots$?

score 776 · Answer 1 · 2026-04-20 03:29:09

776

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The formula for the $n^\text{th}$ term of $\frac{x^2}6 -\frac{x^4}9 + \frac{3x^6}{80} - \frac{71 x^8}{15120} + \frac{ 10361 x^{10}}{10886400} \dots$?

Published on 20 Apr 2026 - 3:29

score 70 · Answer 2 · 2026-04-16 19:39:37

70

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$a_0=0$, $a_{n+1}=a_n-\frac{1}{2}(a_n ^2-a)\rightarrow \sqrt{a}$ using banach's theorem

Published on 16 Apr 2026 - 19:39

score 98 · Answer 3 · 2026-04-14 17:06:07

98

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Why is $\lim_{ n\rightarrow \infty} \frac{1}{n} \sum_{h < n} f(h) = \lim_{ n\rightarrow \infty} f(n) $.

Published on 14 Apr 2026 - 17:06

score 72 · Answer 4 · 2026-04-16 13:16:49

72

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uniform convergence of $g_n(x)=\frac{x}{n^2}e^{-\frac{x}{n}}$

Published on 16 Apr 2026 - 13:16

score 114 · Answer 5 · 2026-04-16 00:53:23

Let $ \ \{a_n \} \ $ be a sequence of non-negative numbers such that $ \ \lim_{n \to \infty} a_n=a \in \mathbb{R} \ $

score 214 · Answer 6 · 2026-05-02 19:52:10

214

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score 194 · Answer 7 · 2026-04-10 17:46:19

194

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score 110 · Answer 8 · 2026-04-15 00:35:28

110

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score 87 · Answer 9 · 2026-04-16 01:45:56

87

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score 57 · Answer 10 · 2026-04-17 10:20:43

57

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score 29 · Answer 11 · 2026-04-12 13:51:31

29

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score 58 · Answer 12 · 2026-04-12 16:09:12

58

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score 78 · Answer 13 · 2026-04-08 19:28:01

78

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score 355 · Answer 14 · 2026-04-15 15:31:02

355

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score 117 · Answer 15 · 2026-04-14 18:03:29

117

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Published on 14 Apr 2026 - 18:03

List Question

The formula for the $n^\text{th}$ term of $\frac{x^2}6 -\frac{x^4}9 + \frac{3x^6}{80} - \frac{71 x^8}{15120} + \frac{ 10361 x^{10}}{10886400} \dots$?

$a_0=0$, $a_{n+1}=a_n-\frac{1}{2}(a_n ^2-a)\rightarrow \sqrt{a}$ using banach's theorem

Why is $\lim_{ n\rightarrow \infty} \frac{1}{n} \sum_{h < n} f(h) = \lim_{ n\rightarrow \infty} f(n) $.

uniform convergence of $g_n(x)=\frac{x}{n^2}e^{-\frac{x}{n}}$

Let $ \ \{a_n \} \ $ be a sequence of non-negative numbers such that $ \ \lim_{n \to \infty} a_n=a \in \mathbb{R} \ $

Is the sum $2+2+2+2+\dotsb$ even?

Question on Interaction of the Alternating Series Test and the Divergence Test

Find $\lim_{n \to \infty} \sum_{k = 2n}^{10n} \frac{1}{k}$

series 0, 6, 13, 20, 27

Prove uniform convergence of $f_n = \frac {x} {1+x^n}$

Convergence of series (Need suggestion)

$g$ is monotonic strictly increasing, continuous in $ [0,\infty)$ and positive function.

Eigenvectors of eigenvectors of eigenvectors of...

Regularization of Exponentially exponential series?

Bessel Series as $-\sum _{k=1}^{\infty } \frac{2 (-1)^n}{\pi ^4 k^4 J_0(k \pi )}$

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