Question

Implicit definition of recursive sequence $\displaystyle a_{n+1} = a_n + \frac{1}{(3 + (-1)^n)^n}$

score 475 · Answer 1 · 2018-04-08 10:38:37

475

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Implicit definition of recursive sequence $\displaystyle a_{n+1} = a_n + \frac{1}{(3 + (-1)^n)^n}$

Published on 08 Apr 2018 - 10:38

score 83 · Answer 2 · 2026-03-26 07:33:18

83

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Computing $\sum_{i = 0}^n \frac{n!}{i!} \mod p$

Published on 26 Mar 2026 - 7:33

score 911 · Answer 3 · 2018-04-09 05:37:15

911

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Sum $\sum(2n+1) × 2^n$

Published on 09 Apr 2018 - 5:37

score 131 · Answer 4 · 2018-04-09 10:06:39

131

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Is $n=13$ the only solution to this: $\pi\left(\sum_{i=1}^n\pi(i)\right)-1=n$.

Published on 09 Apr 2018 - 10:06

score 52 · Answer 5 · 2018-04-09 14:07:22

52

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Is there a way to simplify $\sum_{n=0}^L \binom{L}{n} e^{p^n q^{L-n}}$?

Published on 09 Apr 2018 - 14:07

score 81 · Answer 6 · 2026-03-25 11:20:20

81

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Find $\lim_{n \to \infty}(n - \frac{1}{2^n} \sum_{k=1}^{2^n}\log_{2}(k+2^{n-1}))$ using Riemann sums

Published on 25 Mar 2026 - 11:20

score 83 · Answer 7 · 2018-04-09 19:09:41

83

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Complex Exponentiation using Infinite Summation

Published on 09 Apr 2018 - 19:09

score 51 · Answer 8 · 2026-03-25 03:22:18

51

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How can I use $\sum_{j=0}^{\infty} z^j=\frac{1}{1-z}$ to find a closed form expression for $\sum_{j=0}^{\infty} jz^j$?

Published on 25 Mar 2026 - 3:22

score 66 · Answer 9 · 2018-04-10 07:50:40

66

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Simplifying a summation?

Published on 10 Apr 2018 - 7:50

score 5.5k · Answer 10 · 2018-04-10 14:46:16

5.5k

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Simplify $\sum_{i=1}^n(\sum_{j=i}^n j)$

Published on 10 Apr 2018 - 14:46

score 59 · Answer 11 · 2026-03-26 01:29:15

59

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Closed form expression for $\sum\limits_{k=0}^{n}{n+k \choose k}{n+1 \choose k+1}X^{n-k}Y^{k}$?

Published on 26 Mar 2026 - 1:29

score 670 · Answer 12 · 2026-03-25 03:02:05

670

Views

Formalizing an approach to the sum $\sum_{k=0}^{\infty}ka^k$

Published on 25 Mar 2026 - 3:02

score 122 · Answer 13 · 2026-03-25 07:45:41

122

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Evaluation of the sum $\sum_\limits{a=1}^{p-1} \left\lfloor \frac{\left\lfloor{v/p}\right\rfloor+a}{q}\right\rfloor$

Published on 25 Mar 2026 - 7:45

score 82 · Answer 14 · 2018-04-12 13:48:19

82

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Inequality with natural logarithm I can’t solve

Published on 12 Apr 2018 - 13:48

score 76 · Answer 15 · 2026-03-26 01:28:24

76

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How to calculate this sum with binomials?

Published on 26 Mar 2026 - 1:28

List Question

Implicit definition of recursive sequence $\displaystyle a_{n+1} = a_n + \frac{1}{(3 + (-1)^n)^n}$

Computing $\sum_{i = 0}^n \frac{n!}{i!} \mod p$

Sum $\sum(2n+1) × 2^n$

Is $n=13$ the only solution to this: $\pi\left(\sum_{i=1}^n\pi(i)\right)-1=n$.

Is there a way to simplify $\sum_{n=0}^L \binom{L}{n} e^{p^n q^{L-n}}$?

Find $\lim_{n \to \infty}(n - \frac{1}{2^n} \sum_{k=1}^{2^n}\log_{2}(k+2^{n-1}))$ using Riemann sums

Complex Exponentiation using Infinite Summation

How can I use $\sum_{j=0}^{\infty} z^j=\frac{1}{1-z}$ to find a closed form expression for $\sum_{j=0}^{\infty} jz^j$?

Simplifying a summation?

Simplify $\sum_{i=1}^n(\sum_{j=i}^n j)$

Closed form expression for $\sum\limits_{k=0}^{n}{n+k \choose k}{n+1 \choose k+1}X^{n-k}Y^{k}$?

Formalizing an approach to the sum $\sum_{k=0}^{\infty}ka^k$

Evaluation of the sum $\sum_\limits{a=1}^{p-1} \left\lfloor \frac{\left\lfloor{v/p}\right\rfloor+a}{q}\right\rfloor$

Inequality with natural logarithm I can’t solve

How to calculate this sum with binomials?

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