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Paramanand Singh
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  • Member for 9 years, 2 months
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66 votes

Why does simplifying a function give it another limit

43 votes
Accepted

Ramanujan's approximation for $\pi$

42 votes
Accepted

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

37 votes
Accepted

The Main Theorems of Calculus

37 votes
Accepted

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

34 votes
Accepted

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

31 votes
Accepted

Motivation for/history of Jacobi's triple product identity

30 votes
Accepted

Infinite Integration by Parts

30 votes
Accepted

What even *are* elliptic functions?

28 votes

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

27 votes

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

25 votes

Motivation for Ramanujan's mysterious $\pi$ formula

23 votes
Accepted

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

22 votes

"Gaps" or "holes" in rational number system

21 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 $F$.

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

20 votes
Accepted

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

19 votes
Accepted

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

19 votes
Accepted

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

18 votes

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

18 votes

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

18 votes
Accepted

Taylor's Theorem with Peano's Form of Remainder

17 votes
Accepted

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

17 votes
Accepted

Limits and algebraic simplification

17 votes

Is there a "positive" definition for irrational numbers?

17 votes
Accepted

Perfect understanding of Riemann Sums

15 votes
Accepted

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

14 votes
Accepted

Taking limits on each term in inequality invalid?

14 votes

Prove that $\sin n\theta=n\sin \theta-\frac{n(n^2-1)}{3!}\sin^3\theta+\frac{n(n^2-1)(n^2-3^2)}{5!}\sin^5\theta+\cdots$

14 votes

When converting a Riemann sum to an integral, how does one decide the bounds of the converted Riemann sum?

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