Paramanand Singh's user avatar
Paramanand Singh's user avatar
Paramanand Singh's user avatar
Paramanand Singh
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  • Member for 11 years
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70 votes

Why does simplifying a function give it another limit

52 votes
Accepted

Ramanujan's approximation for $\pi$

45 votes
Accepted

showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$

43 votes
Accepted

How to calculate $\lim_{x \to 0} \frac{x^{6000} - (\sin x)^{6000}}{x^2(\sin x)^{6000}}$?

41 votes
Accepted

The Main Theorems of Calculus

41 votes
Accepted

What even *are* elliptic functions?

37 votes
Accepted

Finding a limit using change of variable- how come it works?

34 votes
Accepted

Infinite Integration by Parts

33 votes

Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$

31 votes
Accepted

Motivation for/history of Jacobi's triple product identity

29 votes

Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$

28 votes

Motivation for Ramanujan's mysterious $\pi$ formula

26 votes

"Gaps" or "holes" in rational number system

24 votes
Accepted

If $K$ be an algebraic extension of $E$ and $E$ be an algebraic extension of $F$ then $K$ is an algebraic extension of $F$.

24 votes
Accepted

Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?

22 votes
Accepted

Taylor's Theorem with Peano's Form of Remainder

22 votes
Accepted

Compute $\lim\limits_{n\to \infty} \int\limits_0^1 x^{2019} \{nx\} dx$

21 votes
Accepted

Analyzing limits problem Calculus (tell me where I'm wrong).

21 votes

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

21 votes
Accepted

series involving $\log \left(\tanh\frac{\pi k}{2} \right)$

18 votes

Proving $f'(1)$ exist for $f$ satisfying $f(xy)=xf(y)+yf(x)$

18 votes

What is the most unusual proof you know that $\sqrt{2}$ is irrational?

17 votes

Is there a "positive" definition for irrational numbers?

17 votes
Accepted

On the general form of the family $\sum_{n=1}^\infty \frac{n^{k}}{e^{2n\pi}-1} $

17 votes

Need help unpacking definitions of $\limsup$, $\liminf$

17 votes
Accepted

Limits and algebraic simplification

17 votes
Accepted

Perfect understanding of Riemann Sums

16 votes
Accepted

Why is the upper Riemann integral the infimum of all upper sums?

16 votes
Accepted

How to evaluate sums in the form $\sum_{k=-\infty}^\infty e^{-\pi n k^2}$

16 votes
Accepted

Taking limits on each term in inequality invalid?

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