Question

Find $\sum_{r=1}^{20} (-1)^r\frac{r^2+r+1}{r!}$.

score 142 · Answer 1 · 2020-08-22 04:15:42

142

Views

Find $\sum_{r=1}^{20} (-1)^r\frac{r^2+r+1}{r!}$.

Published on 22 Aug 2020 - 4:15

score 139 · Answer 2 · 2020-08-22 19:10:43

139

Views

Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

Published on 22 Aug 2020 - 19:10

score 55 · Answer 3 · 2020-08-23 07:55:13

55

Views

For $f(m,n) = (1 - \frac{1}{m}) (1 - \frac{1}{m + 1}) \dots(1 - \frac{1}{n})$, find this sum

Published on 23 Aug 2020 - 7:55

score 549 · Answer 4 · 2020-08-25 10:44:52

549

Views

A summation of a series based on the Fibonacci sequence.

Published on 25 Aug 2020 - 10:44

score 168 · Answer 5 · 2020-08-26 05:24:18

168

Views

Stating and proving a Fibonacci sum: $\sum_{k=1}^{n} \frac{(-1)^{k+1}}{F_k F_{k+1}}=\frac{F_{n}}{F_{n+1}}$

Published on 26 Aug 2020 - 5:24

score 115 · Answer 6 · 2020-08-30 16:38:15

115

Views

Show that: $\binom{n}{3}= \binom{2}{2} + \binom{3}{2} + \binom{4}{2} + \binom{5}{2}+ \ldots + \binom{n-1}{2}$

Published on 30 Aug 2020 - 16:38

score 292 · Answer 7 · 2020-09-01 07:14:18

292

Views

Sum of Telescopic Series

Published on 01 Sep 2020 - 7:14

score 127 · Answer 8 · 2020-09-01 11:03:36

127

Views

Geometric Sequences: What is $r^n$, and how do I find $r$?

Published on 01 Sep 2020 - 11:03

score 325 · Answer 9 · 2020-09-15 08:05:07

325

Views

sum of the series $(1+n)^{1/5} - n^{1/5}$ as $n$ tends to infinity

Published on 15 Sep 2020 - 8:05

score 87 · Answer 10 · 2020-09-25 12:46:22

87

Views

If $f(r)=1+\frac 12 +\frac 13+..+\frac 1r$ and $\sum_{r=1}^n (2r+1)f(r)=P(n)f(n+1)-Q(n)$, where $P$ and $Q$ are polynomial functions.

Published on 25 Sep 2020 - 12:46

score 265 · Answer 11 · 2020-09-26 16:55:06

265

Views

if $S=\sin x+2\sin (2x)+\cdots+n\sin nx$,$C=\cos x +2\cos (2x)+\cdots+n\cos (nx)$

Published on 26 Sep 2020 - 16:55

score 142 · Answer 12 · 2020-09-27 21:41:43

142

Views

The Finite Sum $\sum_{r=1}^{n}\frac{1}{(3r-2)(3r+2)}$ and failure to Telescope

Published on 27 Sep 2020 - 21:41

score 79 · Answer 13 · 2020-10-01 20:41:33

79

Views

Infinite seq. of reals, for every n $ \in \mathbb{N}$ :$(a_{n-1}+a_{n+1})/2\geq a_n$. Prove $ \frac{a_0+a_{n+1}}{2}\geq \frac{a_1+a_2+...+a_n}{n} $

Published on 01 Oct 2020 - 20:41

score 57 · Answer 14 · 2020-10-15 12:01:59

57

Views

Find the value of $(11)+(122)+(1233)+$...$+(12$...$(n-1)n*n)$.

Published on 15 Oct 2020 - 12:01

score 323 · Answer 15 · 2020-11-07 00:30:30

323

Views

Why isn't $\sum_{n=1}^{\infty}(-1)^n$ a telescoping series?

Published on 07 Nov 2020 - 0:30

List Question

Find $\sum_{r=1}^{20} (-1)^r\frac{r^2+r+1}{r!}$.

Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

For $f(m,n) = (1 - \frac{1}{m}) (1 - \frac{1}{m + 1}) \dots(1 - \frac{1}{n})$, find this sum

A summation of a series based on the Fibonacci sequence.

Stating and proving a Fibonacci sum: $\sum_{k=1}^{n} \frac{(-1)^{k+1}}{F_k F_{k+1}}=\frac{F_{n}}{F_{n+1}}$

Show that: $\binom{n}{3}= \binom{2}{2} + \binom{3}{2} + \binom{4}{2} + \binom{5}{2}+ \ldots + \binom{n-1}{2}$

Sum of Telescopic Series

Geometric Sequences: What is $r^n$, and how do I find $r$?

sum of the series $(1+n)^{1/5} - n^{1/5}$ as $n$ tends to infinity

If $f(r)=1+\frac 12 +\frac 13+..+\frac 1r$ and $\sum_{r=1}^n (2r+1)f(r)=P(n)f(n+1)-Q(n)$, where $P$ and $Q$ are polynomial functions.

if $S=\sin x+2\sin (2x)+\cdots+n\sin nx$,$C=\cos x +2\cos (2x)+\cdots+n\cos (nx)$

The Finite Sum $\sum_{r=1}^{n}\frac{1}{(3r-2)(3r+2)}$ and failure to Telescope

Infinite seq. of reals, for every n $ \in \mathbb{N}$ :$(a_{n-1}+a_{n+1})/2\geq a_n$. Prove $ \frac{a_0+a_{n+1}}{2}\geq \frac{a_1+a_2+...+a_n}{n} $

Find the value of $(11)+(122)+(1233)+$...$+(12$...$(n-1)n*n)$.

Why isn't $\sum_{n=1}^{\infty}(-1)^n$ a telescoping series?

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