91,972 reputation
1077139
bio website
location Kolkata, India
age
visits member for 2 years, 1 month
seen 2 hours ago

Jul
19
answered How to find $\sum_{r=1}^{n} r^2\cos {(r\theta)}$
Jul
19
comment Elementary Application of Legendre Symbol
math.stackexchange.com/questions/609560/…
Jul
19
comment How to find $\sum_{r=1}^{n} r^2\cos {(r\theta)}$
math.stackexchange.com/questions/117114/…
Jul
19
answered Integrate $\int \sin^4x \cos^2x dx$
Jul
19
comment Prove of a Pythagorian Triple
cut-the-knot.org/pythagoras/pythTripleDiv.shtml
Jul
19
comment Nth value of Function
Use en.wikipedia.org/wiki/Recurrence_relation#Solving
Jul
19
answered How to get a partial sum formula
Jul
19
comment Area of the quadrilateral within a triangle
Which three : $$BEF, BFC, CDF$$ or $ABC$ and other two?
Jul
19
comment Limit of factorial how to continue
This is <$$\frac {n+1}{2^n}\frac{n+1}{2^{(n-1)!}}$$
Jul
19
comment Limit of factorial how to continue
$$\frac{(n+1)^{n+1}n!}{2^{n\cdot n!}}=\frac{(n+1)^n \cdot (n+1)!}{(2^{n\cdot (n-1)!})^n}$$ $$=\left(\frac{n+1}{2^n}\right)^n\frac{(n+1)!}{2^{n\cdot (n-1)!}}$$
Jul
19
answered Problem about moving sides of triangle
Jul
19
revised Evaluate $\int \frac{1}{(2x+1)\sqrt {x^2+7}}dx$
added 213 characters in body
Jul
19
comment I don't understand the solution to this limit.
en.wikipedia.org/wiki/Geometric_progression#Derivation
Jul
19
answered Evaluate $\int \frac{1}{(2x+1)\sqrt {x^2+7}}dx$
Jul
19
comment $\lim_{n \rightarrow \infty} \frac{3}{n} \sum_{k=1}^n \left(\frac{2n+3k}{n} \right)^2$
@ClaudeLeibovici, There was a typo, it should be : $$3\int_0^1 (2+3x)^2\ dx=\frac{(2+3x)^3|_0^1}3=\frac{5^3-2^3}3 $$
Jul
19
comment $\lim_{n \rightarrow \infty} \frac{3}{n} \sum_{k=1}^n \left(\frac{2n+3k}{n} \right)^2$
@Yaldc, See also: math.stackexchange.com/questions/469885/…
Jul
19
answered $\lim_{n \rightarrow \infty} \frac{3}{n} \sum_{k=1}^n \left(\frac{2n+3k}{n} \right)^2$
Jul
19
revised Derive $3 \tan^{−1} (x+ ((1 + x^2)^.5))$
added 146 characters in body
Jul
19
answered Derive $3 \tan^{−1} (x+ ((1 + x^2)^.5))$
Jul
19
answered Prove $n^4 \equiv 1 \pmod{5}$