Skip to main content
Mathematics
Dhrubajyoti Bhattacharjee's user avatar
Dhrubajyoti Bhattacharjee's user avatar
Dhrubajyoti Bhattacharjee's user avatar
Dhrubajyoti Bhattacharjee
  • Member for 4 years, 4 months
  • Last seen more than a month ago
  • India
Profile Activity
Stats
1,265
reputation
16k
reached
1
answer
46
questions
Communities
View all
About

Miles to go before I sleep..

Badges
View all badges
This user doesn’t have any gold badges yet.
5
silver badges
15
bronze badges
Top tags
View all tags
3
Score
4
Posts
9
Posts %
0
Score
11
Posts
23
Posts %
0
Score
8
Posts
17
Posts %
0
Score
8
Posts
17
Posts %
0
Score
7
Posts
15
Posts %
0
Score
7
Posts
15
Posts %
Top posts
View all questions and answers
12
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
Jun 16, 2020
10
Evaluate: $\int_0^1 \sqrt{x+\sqrt{x^2+\sqrt{x^3+\cdots}}}\, dx. $
Jul 22, 2020
6
If $f(x)=\sum_{n=1}^{50}(x-n)^{51n-n^2},$ then find $\frac{f(51)}{f'(51)}.$
Aug 17, 2020
5
Find all possible positive integers $x$ and $y$ such that the equation: $(x+y)(x-y)=\frac{(y+1)(y-1)}{24}$ is satisfied.
May 28, 2020
5
If $a, b, c\in\mathbb R^+, $ then prove that $a^3b+b^3c+c^3a\ge abc(a+b+c) .$
Jun 3, 2020
5
If $a+b+c=0, ab+bc+ca=1$ and $abc=1,$ then find the value of $\frac ab+\frac bc+\frac ca.$
Jun 14, 2020
4
If $c\in\mathbb R,$ then prove that $\sin(x)+\sin(cx)$ is periodic iff $c\in\mathbb Q.$
May 31, 2020
4
If a sequence $\langle a_n\rangle$ is such that $a_1a_2=1, a_2a_3=2, \ldots$ and $\lim\frac{a_n}{a_{n+1}}=1.$ Then find $|a_1|.$
Jul 21, 2020
4
If $a, b, c, d\in\mathbb R^+, $ then prove that $\displaystyle\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+a}+\frac{d-a}{a+b}\ge 0.$
Jun 12, 2020
3
Evaluate: $\lim_{x\to y} \frac{x^y-y^x}{x^x-y^y},$ without using L'Hospital's rule.
May 24, 2020