Question

Prove common ratio of GP from a equation

score 160 · Answer 1 · 2026-03-25 01:16:34

160

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Prove common ratio of GP from a equation

Published on 25 Mar 2026 - 1:16

score 87 · Answer 2 · 2026-04-12 15:07:38

87

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When is it necessary to increase $N$ when $\epsilon$ decreases for Cauchy sequences?

Published on 12 Apr 2026 - 15:07

score 491 · Answer 3 · 2026-04-13 02:30:45

491

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cauchy sequences and their relation to sums of distances in metric spaces

Published on 13 Apr 2026 - 2:30

score 95 · Answer 4 · 2026-04-14 17:44:26

95

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Does $\sum _{n=1}^{\infty }\left(a_n\:+\:b_n\right)^2$ converges?

Published on 14 Apr 2026 - 17:44

score 653 · Answer 5 · 2026-04-11 07:33:05

653

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Finding the Maclaurin series of a given function knowing another Maclaurin series

Published on 11 Apr 2026 - 7:33

score 696 · Answer 6 · 2026-04-15 09:28:06

696

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For what value of $\alpha$, does this series converge?

Published on 15 Apr 2026 - 9:28

score 35 · Answer 7 · 2026-04-09 10:42:38

35

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Convergence of Series with Ratio Test

Published on 09 Apr 2026 - 10:42

score 147 · Answer 8 · 2026-04-15 05:15:46

147

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Proof of $(1+x)^\alpha$ converges to its Taylor expansion at $x_0=0$ when $-1<\alpha<0$ and $x=1$

Published on 15 Apr 2026 - 5:15

score 170 · Answer 9 · 2026-04-17 11:27:02

170

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$x_1=1,x_n=x_{n+1}+\ln (1+x_{n+1})$, prove $x_n\leq\frac{1}{2^{n-2}}$.

Published on 17 Apr 2026 - 11:27

score 59 · Answer 10 · 2026-04-15 21:51:53

59

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Positive sequence $\{a_n\}$, $a_{n+1}=-\sqrt{a_n}+1, a_1\in{(\frac12,1)}$. Prove $a_{2n+1}+a_{2n+2}<a_{2n-1}+a_{2n}$.

Published on 15 Apr 2026 - 21:51

score 59 · Answer 11 · 2026-04-14 23:23:57

59

Views

Complete series expansion of $\frac{1}{1+f(x)}$

Published on 14 Apr 2026 - 23:23

score 68 · Answer 12 · 2026-04-18 02:56:42

68

Views

$I(x_1, x_2, . . . , x_6) = 2x_1 + 4x_2 + 6x_3 + 8x_4 + 10x_5 + 12x_6 \mod 10$ is the invariant

Published on 18 Apr 2026 - 2:56

score 85 · Answer 13 · 2026-04-15 23:27:53

85

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Find sequence $(a_n)$ and $(b_n)$

Published on 15 Apr 2026 - 23:27

score 64 · Answer 14 · 2026-04-29 12:51:59

64

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Determine all limits of subsequences of $|\lambda \alpha^n +\mu \bar{\alpha}^n|$ (assume $|\alpha|>1$)

Published on 29 Apr 2026 - 12:51

score 75 · Answer 15 · 2026-04-12 15:24:31

75

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Given the sum of this series, find the sum of another series.

Published on 12 Apr 2026 - 15:24

List Question

Prove common ratio of GP from a equation

When is it necessary to increase $N$ when $\epsilon$ decreases for Cauchy sequences?

cauchy sequences and their relation to sums of distances in metric spaces

Does $\sum _{n=1}^{\infty }\left(a_n\:+\:b_n\right)^2$ converges?

Finding the Maclaurin series of a given function knowing another Maclaurin series

For what value of $\alpha$, does this series converge?

Convergence of Series with Ratio Test

Proof of $(1+x)^\alpha$ converges to its Taylor expansion at $x_0=0$ when $-1<\alpha<0$ and $x=1$

$x_1=1,x_n=x_{n+1}+\ln (1+x_{n+1})$, prove $x_n\leq\frac{1}{2^{n-2}}$.

Positive sequence $\{a_n\}$, $a_{n+1}=-\sqrt{a_n}+1, a_1\in{(\frac12,1)}$. Prove $a_{2n+1}+a_{2n+2}<a_{2n-1}+a_{2n}$.

Complete series expansion of $\frac{1}{1+f(x)}$

$I(x_1, x_2, . . . , x_6) = 2x_1 + 4x_2 + 6x_3 + 8x_4 + 10x_5 + 12x_6 \mod 10$ is the invariant

Find sequence $(a_n)$ and $(b_n)$

Determine all limits of subsequences of $|\lambda \alpha^n +\mu \bar{\alpha}^n|$ (assume $|\alpha|>1$)

Given the sum of this series, find the sum of another series.

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