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Mathematics
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C.S.'s user avatar
C.S.'s user avatar
C.S.
  • Member for 11 years
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Our true needs are deeper – yet in our modern society most of us reflexively and relentlessly pursue wealth, consumer goods and admiration. We have learned from Perelman's mathematics. Perhaps we should also pause to reflect on ourselves and learn from Perelman's attitude towards life. : Bill Thurston

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question
23
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
Jul 29, 2016
answer
20
Can the group $\mathbb Z \times \mathbb Z$ be written as union of finitely many proper subgroups of it?
Sep 26, 2019
answer
17
Prove: $\sin (\tan x) \geq {x}$
Jan 18, 2014
question
15
How does one evaluate $\int \frac{\sin(x)}{\sin(5x)} \ dx$
Oct 19, 2014
answer
14
Find the value of: $\sum_{n=1}^{50}n(n!)$
May 1, 2015
question
13
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
Oct 4, 2017
answer
11
Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$
Jul 24, 2018
answer
9
Sum of $50$ terms of $\cot^{-1}3+\cot^{-1}7+\cot^{-1}13+\cot^{-1}21+.....$
Dec 15, 2018
answer
9
Alternating sum of binomial coefficients multiplied by (1/k+1)
Oct 8, 2014
answer
8
How to calculate $\lim_{x\to0} \frac{\ln(1+x)+\ln(1-x)}{x^2}$?
Nov 1, 2017
Top network posts
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235
If $f$ is infinitely differentiable then $f$ coincides with a polynomial
94
Recovering accidentally deleted files
56
Not especially famous, long-open problems which anyone can understand
51
Function satisfying $f^{-1} =f'$
49
Not especially famous, long-open problems which anyone can understand