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Samrat Mukhopadhyay

I am always an avid lover of Mathematics. I am now a PhD student on Signal Processing. I have started learning bits of real Analysis, general topology, functional analysis and measure theory. I want to know the subjects more deeply and thoroughly. I am currently following the books by Rudin for analysis, Munkres for topology, Kreyzig for functional analysis and schilling for measure theory. Hope to know more.

These daunting busy days are keeping me from coming to this site. But I will return.

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48 How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$? Jul 25 '13
19 How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$? Aug 5 '13
19 $\sum a_n$ converges $\implies\ \sum a_n^2$ converges? May 14 '15
18 Prove that $ n < 2^{n}$ for all natural numbers $n$. Jul 22 '13
17 How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$? Jul 25 '13
17 What functions satisfy such equation? Feb 20 '15
15 Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? Jul 24 '13
14 Prove that $z_{n+1} = \frac12 \left(z_n +\frac{1}{z_n} \right) $ converges to $1$ Jun 29 '13
14 Are eigenvalues of the limit of a sequence of matrices limits of eigenvalue sequences? Jul 2 '15
11 Nested Radical of Ramanujan Aug 3 '13
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