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Ishan Banerjee
  • Member for 9 years, 6 months
  • Last seen more than 6 years ago
39 votes

The generating function for the Fibonacci numbers

14 votes
Accepted

What is wrong with this problem

12 votes

Evaluating :$\int\cot^{-1} (x^2+x+1)dx $

12 votes
Accepted

Evaluating the integral $\int_0^1\arctan(1-x+x^2)dx$

11 votes
Accepted

Computing $\lim_{n\to\infty}n\sum_{k=1}^n\left( \frac{1}{(2k-1)^2} - \frac{3}{4k^2}\right)$

11 votes

How do I derive $1 + 4 + 9 + \cdots + n^2 = \frac{n (n + 1) (2n + 1)} 6$

10 votes
Accepted

Rational points on a circle with centre $(\pi, e)$

9 votes
Accepted

A question about the arctangent addition formula.

8 votes
Accepted

Proving that one infinite series is equal to another.

8 votes
Accepted

Does $\frac{3}{1\cdot 2} - \frac{5}{2\cdot 3} + \frac{7}{3\cdot 4} - ...$ Converges?

8 votes
Accepted

Good ways to integrate $\int_0^1 x^{k+1} (1-x)^k dx$?

8 votes

2013th derivative of a trigonometric function

7 votes

Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$

7 votes

Evaluating $\lim \limits_{n\to \infty}\,\,\, n\!\! \int\limits_{0}^{\pi/2}\!\! \left(1-\sqrt [n]{\sin x} \right)\,\mathrm dx$

7 votes

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.

6 votes

how can I show that the sequence $x_{n}=\frac{n}{n^{2}+1}+\frac{n}{n^2+2}+...+\frac{n}{n^2+n},n=1,2,...$ converges?

6 votes

Improper definite integral

6 votes
Accepted

Why is $\int\limits_{1}^{n} \log x \,dx \le \sum\limits_{x = 1}^{n}\log x$?

6 votes
Accepted

Need a hint to evaluate the indefinite integral $\int\frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$?

5 votes

Alternative solutions to $\lim_{n\to\infty} \frac{1}{\sqrt{n}}\int_{ 1/{\sqrt{n}}}^{1}\frac{\ln(1+x)}{x^3}\mathrm{d}x$

5 votes

Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$

5 votes

Find the nth term of a recursive sequence

5 votes
Accepted

Solution of Ordinary Differential equation

5 votes
Accepted

Calculate:$\int \frac{1}{(x+1)^\frac{3}{4}(x+2)^{\frac{5}{4}}}\ dx$

5 votes
Accepted

Finding the coefficient of $ x^n $ in the expansion of $ { ({\ log_e (1+x) })^2 } $

5 votes
Accepted

Dirac delta function of x squared

4 votes
Accepted

a question about integral proof: $\lim_{n\to \infty} \int_{0}^\infty {n\cdot {\ln(1+{f(x)\over n}}})dx=\int_{0}^\infty f(x)dx$

4 votes
Accepted

Series with cosine explanation

4 votes

Limit of $\frac{1}{n}\sum\limits_{i =2}^n \frac{1}{\ln i}$ as $n \to \infty$

4 votes

Convergence of the sequence $(1+\frac{1}{n})(1+\frac{2}{n})\cdots(1+\frac{n}{n})$

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