User lab bhattacharjee - Mathematics Stack Exchange

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	28,118 reputation	bio	website		visits	member for	11 months
12347 badges		location	Kolkata, India		seen	2 hours ago

166

265

votes

115

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13

kviews

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

may 6 at 4:59 Jori Mäntysalo 31

69

157

votes

13

answers

11

kviews

Is value of $\pi = 4$?

geometry analysis pi fake-proofs

1d ago exploringnet 2,255

15

42

votes

12

answers

3

kviews

All natural numbers are equal.

induction fake-proofs

may 8 at 12:01 Lucian Depold 121

15

41

votes

3

answers

535

views

Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

sequences-and-series reference-request fourier-series modular-forms elliptic-functions

may 14 at 3:00 Marko Riedel 1,839

26

39

votes

4

answers

1

kviews

Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even

homework calculus real-analysis integration

oct 21 at 3:06 user17762 75.9k

11

39

votes

4

answers

2

kviews

$x$, $y$, $x+y$ and $x-y$ are prime numbers. What is their sum?

elementary-number-theory prime-numbers

dec 4 at 23:22 Community♦ 1

10

36

votes

3

answers

942

views

Triangular Factorials

number-theory diophantine-equations

nov 23 at 19:53 zyx 10.9k

9

35

votes

4

answers

3

kviews

Value of $\sum\limits_n x^n$

sequences-and-series algebra-precalculus faq

jan 3 '12 at 15:23 Quixotic 7,920

12

33

votes

3

answers

607

views

Prove $(\dfrac{2}{5})^{\frac{2}{5}}<\ln{2}$

inequality logarithms

may 6 at 8:12 Martin Sleziak 20.3k

14

31

votes

5

answers

884

views

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

sequences-and-series trigonometry pi

may 7 at 15:34 robjohn♦ 59.2k

12

23

votes

1

answer

1

kviews

Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer

number-theory

apr 9 '11 at 12:39 Amir Hossein 1,315

7

21

votes

4

answers

446

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Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$

real-analysis algebra-precalculus recurrence-relations

feb 12 at 16:25 A.P. 158

6

20

votes

3

answers

409

views

Finding the value of $\sum\limits_{k=0}^{\infty}\frac{2^{k}}{2^{2^{k}}+1}$

sequences-and-series summation

apr 10 at 9:53 azimut 5,426

6

19

votes

5

answers

525

views

Power Series Summation Formula

power-series

jan 22 at 19:30 Dave L. Renfro 6,586

7

18

votes

4

answers

1

kviews

Seems that I just proved $2=4$.

fake-proofs paradox

may 12 at 9:25 Martin Sleziak 20.3k

6

18

votes

4

answers

582

views

Find $\lim\limits_{n \rightarrow \infty}\dfrac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$

calculus limit

may 13 at 17:45 Cortizol 1,314

5

18

votes

6

answers

895

views

Integral solution for $|x | + | y | + | z | = 10$

number-theory diophantine-equations

nov 12 at 4:11 LevanDokite 79

4

18

votes

5

answers

785

views

Integer solutions to $\sqrt{a} + \sqrt{b} = \sqrt{c}$

number-theory

dec 1 at 22:37 Hagen von Eitzen 41.8k

5

17

votes

1

answer

588

views

Expressing $2002^{2002}$ as a sum of cubes

number-theory

jun 27 at 3:43 Alex Hirzel 223

3

17

votes

3

answers

432

views

Why can't $\sqrt{2}^{\sqrt{2}{^\sqrt{2}{^\cdots}}}>2$?

sequences-and-series analysis limit convergence

nov 9 at 4:56 Oleg567 756

6

17

votes

8

answers

719

views

Comparing $2013!$ and $1007^{2013}$

elementary-number-theory inequality

may 11 at 11:08 Amr 8,788

5

17

votes

9

answers

616

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Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$

algebra-precalculus problem-solving

17h ago RecklessReckoner 1,269

5

16

votes

1

answer

135

views

To prove that $2^{3n}+2^n +1$ is not a perfect square.

algebra-precalculus elementary-number-theory contest-math

may 15 at 4:49 Inceptio 4,350

6

16

votes

2

answers

195

views

Prove that there isn't a polynomial with $\text {f(x)}^{13} = {(x-1)}^{143}+(x+1)^{2002}$

abstract-algebra polynomials

may 14 at 15:08 Mark Bennet 9,818

2

16

votes

6

answers

427

views

$\log_9 71$ or $\log_8 61$

algebra-precalculus inequality logarithms

nov 3 at 0:23 Daniel Littlewood 2,638

13

15

votes

8

answers

1

kviews

How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$

homework sequences-and-series

apr 24 at 18:56 glebovg 2,295

6

15

votes

1

answer

201

views

$x^3-3x-3=0$, prove that $10^x<127$

inequality logarithms taylor-expansion

may 7 at 19:15 Hagen von Eitzen 41.8k

7

15

votes

2

answers

273

views

$(x-a)(x-b)(x-c)(x-d)=ex$

number-theory elementary-number-theory diophantine-equations

mar 20 at 8:32 Tito Piezas III 2,373

9

15

votes

2

answers

238

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How to find the value of $\sin{\dfrac{\pi}{14}}+6\sin^2{\dfrac{\pi}{14}}-8\sin^4{\dfrac{\pi}{14}}$

trigonometry

apr 18 at 13:59 TMM 7,156

4

14

votes

10

answers

962

views

Why isn't $\lim_{x\to\infty}(1+\frac{1}{x})^{x}= 1$?

limit exponential-function

apr 23 at 23:02 ludwika 1

lab bhattacharjee

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