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Paramanand Singh
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2,291 Answers

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60
Why does simplifying a function give it another limit
Jun 12 '16 at 1:14
38
How to calculate $\lim_{x \to 0} \frac{x^{6000} - (\sin x)^{6000}}{x^2(\sin x)^{6000}}$?
May 15 '16 at 16:38
35
Ramanujan's approximation for $\pi$
Sep 7 '14 at 5:39
33
The Main Theorems of Calculus
May 16 '16 at 8:05
29
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
Oct 20 '13 at 8:11
29
Motivation for/history of Jacobi's triple product identity
Jul 12 '13 at 8:57
27
Infinite Integration by Parts
Feb 15 '17 at 4:53
25
Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$
Oct 3 '17 at 11:52
22
Finding a limit using change of variable- how come it works?
Dec 18 '14 at 7:12
21
Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$
May 25 '16 at 4:01
20
Motivation for Ramanujan's mysterious $\pi$ formula
Jul 2 '13 at 5:16
19
“Gaps” or “holes” in rational number system
Apr 30 at 3:15
18
What even *are* elliptic functions?
Oct 10 '19 at 15:19
18
The derivative of $e^x$ using the definition of derivative as a limit and the definition $e^x = \lim_{n\to\infty}(1+x/n)^n$, without L'Hôpital's rule
Oct 27 '13 at 10:41
17
Proving $f'(1)$ exist for $f$ satisfying $f(xy)=xf(y)+yf(x)$
Jan 10 '17 at 4:49
17
Limits and algebraic simplification
Sep 23 '17 at 15:27
17
Is there a “positive” definition for irrational numbers?
Sep 6 '16 at 11:35
17
What is the most unusual proof you know that $\sqrt{2}$ is irrational?
Jun 14 '15 at 5:03
16
Compute $\lim\limits_{n\to \infty} \int\limits_0^1 x^{2019} \{nx\} dx$
Jan 30 at 8:37
16
Taylor's Theorem with Peano's Form of Remainder
Jun 2 '16 at 5:51
16
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
Jan 30 '17 at 8:34
15
Perfect understanding of Riemann Sums
Oct 27 '18 at 6:43
15
series involving $\log \left(\tanh\frac{\pi k}{2} \right)$
May 21 '16 at 3:50
14
When converting a Riemann sum to an integral, how does one decide the bounds of the converted Riemann sum?
May 20 at 9:09
14
If $K$ be an algebraic extension of $E$ and $E$ be an algebraic extension of $F$ then $K$ is an algebraic extension of $F$.
Apr 20 '17 at 3:52
14
On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $
Sep 27 '16 at 20:56
14
If $f$ is continuous and $f(x+y)=f(x)f(y)$, then $\lim\limits_{x \rightarrow 0} \frac{f(x)-f(0)}{x}$ exists
Aug 8 '16 at 9:19
13
Fibonacci sum: $\sum\limits_{k\ge0}\frac{F_{2k+1}}{2k+1}\left(\frac{2+2\sqrt{2}}{1+\sqrt{\frac{17+8\sqrt{2}}{5}}}\right)^{2k+1}(-\frac{1}{5})^k$
Nov 13 '19 at 9:11
13
Analyzing limits problem Calculus (tell me where I'm wrong).
May 13 '16 at 14:34
13
How can I calculate $\lim_{n \rightarrow \infty} \frac {e^n(2n)!}{(4n)^nn!}$
Jul 11 '18 at 15:31
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