Question

$\sum_{n=1}^{2016}\left\lfloor\frac{\sqrt n}{10}\right\rfloor$ in 2 minutes

score 322 · Answer 1 · 2026-04-16 00:27:17

322

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$\sum_{n=1}^{2016}\left\lfloor\frac{\sqrt n}{10}\right\rfloor$ in 2 minutes

Published on 16 Apr 2026 - 0:27

score 155 · Answer 2 · 2026-05-11 03:49:21

155

Views

How can I work out this divergent sum?

Published on 11 May 2026 - 3:49

score 125 · Answer 3 · 2026-04-14 22:23:02

125

Views

Any Idea of algorithm

Published on 14 Apr 2026 - 22:23

score 54 · Answer 4 · 2026-04-16 19:57:58

54

Views

Prove $\sum_{k=p}^{q} c = (q-p+1)c$ where $p$,$q$ are integers, $p$ less than or equal to $q$ .

Published on 16 Apr 2026 - 19:57

score 91 · Answer 5 · 2026-04-11 23:06:46

91

Views

Estimating the Lower Bound of A Summation Related to Probability

Published on 11 Apr 2026 - 23:06

score 77 · Answer 6 · 2026-04-15 23:03:39

Help simplifying the expression $\bigg(-1+{n+1 \choose 2}\bigg)+{n+1 \choose 2}+\bigg(1+{n+1 \choose 2}\bigg)+\cdots+\bigg(n-2+{n+1 \choose 2}\bigg)$

score 92 · Answer 7 · 2026-04-13 12:46:14

92

Views

A family of generating functions related to generalized harmonic numbers and power functions.

Published on 13 Apr 2026 - 12:46

score 2.5k · Answer 8 · 2026-04-14 20:41:19

2.5k

Views

How many pairwise distinct sums are there in a finite set of consecutive Integers?

Published on 14 Apr 2026 - 20:41

score 96 · Answer 9 · 2026-04-17 00:42:07

96

Views

Show that $\lim_{m\rightarrow\infty}4^{-m}\sum\limits_{j=0}^{\lfloor m/2\rfloor}(-1)^j\binom{m}{j}\binom{3m-4j}{2m-4j}=1$

Published on 17 Apr 2026 - 0:42

score 1.2k · Answer 10 · 2026-04-17 05:28:07

1.2k

Views

Evaluate $\sum_{j=0}^n(-1)^{n+j}{n\choose j}{{n+j}\choose j}\frac{1}{(j+1)^2}$

Published on 17 Apr 2026 - 5:28

score 118 · Answer 11 · 2026-04-16 14:57:45

118

Views

Short "beautiful" proof for simple fact wanted

Published on 16 Apr 2026 - 14:57

score 86 · Answer 12 · 2026-04-16 04:48:07

86

Views

Is the value of $\sum_{x=0}^{\infty}\frac{\cos(\pi x)}{x!}=1/e$?

Published on 16 Apr 2026 - 4:48

score 51 · Answer 13 · 2026-04-28 17:37:56

51

Views

How to express sum of areas of triangular elements meeting a criteria

Published on 28 Apr 2026 - 17:37

score 2.8k · Answer 14 · 2026-04-10 02:59:48

2.8k

Views

Can every number be represented as a sum of different reciprocal numbers?

Published on 10 Apr 2026 - 2:59

score 69 · Answer 15 · 2026-04-11 23:00:04

69

Views

Limit in sum and fraction

Published on 11 Apr 2026 - 23:00

List Question

$\sum_{n=1}^{2016}\left\lfloor\frac{\sqrt n}{10}\right\rfloor$ in 2 minutes

How can I work out this divergent sum?

Any Idea of algorithm

Prove $\sum_{k=p}^{q} c = (q-p+1)c$ where $p$,$q$ are integers, $p$ less than or equal to $q$ .

Estimating the Lower Bound of A Summation Related to Probability

Help simplifying the expression $\bigg(-1+{n+1 \choose 2}\bigg)+{n+1 \choose 2}+\bigg(1+{n+1 \choose 2}\bigg)+\cdots+\bigg(n-2+{n+1 \choose 2}\bigg)$

A family of generating functions related to generalized harmonic numbers and power functions.

How many pairwise distinct sums are there in a finite set of consecutive Integers?

Show that $\lim_{m\rightarrow\infty}4^{-m}\sum\limits_{j=0}^{\lfloor m/2\rfloor}(-1)^j\binom{m}{j}\binom{3m-4j}{2m-4j}=1$

Evaluate $\sum_{j=0}^n(-1)^{n+j}{n\choose j}{{n+j}\choose j}\frac{1}{(j+1)^2}$

Short "beautiful" proof for simple fact wanted

Is the value of $\sum_{x=0}^{\infty}\frac{\cos(\pi x)}{x!}=1/e$?

How to express sum of areas of triangular elements meeting a criteria

Can every number be represented as a sum of different reciprocal numbers?

Limit in sum and fraction

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