# Ishan Banerjee

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 14 What is wrong with this problem 11 Evaluating :$\int\cot^{-1} (x^2+x+1)dx$ 11 Computing $\lim_{n\to\infty}n\sum_{k=1}^n\left( \frac{1}{(2k-1)^2} - \frac{3}{4k^2}\right)$ 10 how do I derive $1 + 4 + 9 + \cdots + n^2 = \frac{n (n + 1) (2n + 1)} 6$ 8 Proving that one infinite series is equal to another.

# 4,407 Reputation

 +10 Evaluating the integral $\int_0^1\arctan(1-x+x^2)dx$ +5 Tangent space to lie group at identity. +15 Problem with understanding proof of Van Kampen's theorem +10 Prove that there are infinitely many natural numbers $n$, such that $n(n+1)$ can be expressed as sum of two positive squares in two distinct ways.

# 18 Questions

 14 Evaluating $\int_0^{\infty}\frac{e^{-x}}{1+x^2}dx$ 13 Finding $\int^1_0 \frac{\log(1+x)}{x}dx$ without series expansion 12 $AB-BA=I$ having no solutions 8 Value of $\sum_{k=1}^{\infty}\frac{1}{k^2+a^2}$ 7 Limit of $a_{k+1}=\dfrac{a_k+b_k}{2}$, $b_{k+1}=\sqrt{a_kb_k}$?

# 83 Tags

 121 calculus × 45 19 convergence × 8 87 sequences-and-series × 28 18 combinatorics × 9 57 integration × 20 17 elementary-number-theory × 12 56 real-analysis × 28 17 trigonometry × 7 55 limits × 25 16 analysis × 8

# 2 Accounts

 Mathematics 4,407 rep 1733 Stack Overflow 101 rep