Question

Prime divisors of the sequence terms $a_n=a\cdot 2017^n+b\cdot 2016^n$

score 342 · Answer 1 · 2026-04-17 04:25:26

342

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Prime divisors of the sequence terms $a_n=a\cdot 2017^n+b\cdot 2016^n$

Published on 17 Apr 2026 - 4:25

score 79 · Answer 2 · 2026-04-17 04:42:15

79

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Show that $\ln\left(1+3x + 2x^2\right) = 3x - \frac{5x^2}{2} + \frac{9x^3}{3} -\cdots + \left(-1\right)^{n-1}\frac{2^n+1}{n}x^n+\cdots$

Published on 17 Apr 2026 - 4:42

score 97 · Answer 3 · 2026-05-14 20:08:47

97

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Power series solutions

Published on 14 May 2026 - 20:08

score 32 · Answer 4 · 2026-04-16 17:15:56

32

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prove that the sequence given by recurrence converges

Published on 16 Apr 2026 - 17:15

score 307 · Answer 5 · 2026-04-13 10:49:16

307

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Recursive definition of this sequence

Published on 13 Apr 2026 - 10:49

score 120 · Answer 6 · 2026-04-15 07:48:23

120

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Convergence and Limit of the infinite series

Published on 15 Apr 2026 - 7:48

score 91 · Answer 7 · 2026-04-16 04:48:25

91

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For which $a , b , c$ $\sum \frac{a^n}{(\log n)^c n^b}$ would be divergent?

Published on 16 Apr 2026 - 4:48

score 60 · Answer 8 · 2026-04-15 21:38:45

60

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Does $f_0=x,f_{n+1}(x)=e^{1/f_n(x)}$ converge to $1/W(1)$?

Published on 15 Apr 2026 - 21:38

score 521 · Answer 9 · 2026-04-17 15:54:15

521

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Compute $1^{1/3}+2^{1/3}.........7999^{1/3}$

Published on 17 Apr 2026 - 15:54

score 96 · Answer 10 · 2026-04-15 15:23:31

96

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Limit of $a_{n}^{2}$ when the sequence is recursive

Published on 15 Apr 2026 - 15:23

score 94 · Answer 11 · 2026-04-14 20:54:35

94

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Why does $\ell_p$ have infinitely many linearly independent vectors when it equals its double dual (and so is finite dimensional)?

Published on 14 Apr 2026 - 20:54

score 153 · Answer 12 · 2026-04-15 20:50:03

153

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Mathematical Induction: Addition of uneven cubes

Published on 15 Apr 2026 - 20:50

score 131 · Answer 13 · 2026-05-04 22:04:50

131

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$f(x) = \tan^{-1}(x)$ || Is there any easy method to show that the sequence [$f^n(0)$] is unbounded?

Published on 04 May 2026 - 22:04

score 91 · Answer 14 · 2026-04-13 10:57:05

91

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Convergence of integrals by examining the sum

Published on 13 Apr 2026 - 10:57

score 183 · Answer 15 · 2026-05-10 15:10:22

183

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When is $(\frac{v_1}{1}+\frac{v_2}{2}+ \dots \frac{v_p}{p})+(\frac{v_1}{p+1}+\frac{v_2}{p+2}+\dots \frac{v_p}{2p})+\dots$ equal to zero?

Published on 10 May 2026 - 15:10

List Question

Prime divisors of the sequence terms $a_n=a\cdot 2017^n+b\cdot 2016^n$

Show that $\ln\left(1+3x + 2x^2\right) = 3x - \frac{5x^2}{2} + \frac{9x^3}{3} -\cdots + \left(-1\right)^{n-1}\frac{2^n+1}{n}x^n+\cdots$

Power series solutions

prove that the sequence given by recurrence converges

Recursive definition of this sequence

Convergence and Limit of the infinite series

For which $a , b , c$ $\sum \frac{a^n}{(\log n)^c n^b}$ would be divergent?

Does $f_0=x,f_{n+1}(x)=e^{1/f_n(x)}$ converge to $1/W(1)$?

Compute $1^{1/3}+2^{1/3}.........7999^{1/3}$

Limit of $a_{n}^{2}$ when the sequence is recursive

Why does $\ell_p$ have infinitely many linearly independent vectors when it equals its double dual (and so is finite dimensional)?

Mathematical Induction: Addition of uneven cubes

$f(x) = \tan^{-1}(x)$ || Is there any easy method to show that the sequence [$f^n(0)$] is unbounded?

Convergence of integrals by examining the sum

When is $(\frac{v_1}{1}+\frac{v_2}{2}+ \dots \frac{v_p}{p})+(\frac{v_1}{p+1}+\frac{v_2}{p+2}+\dots \frac{v_p}{2p})+\dots$ equal to zero?

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