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Jack's wasted life
  • Member for 8 years, 6 months
  • Last seen more than a week ago
24 votes
Accepted

If $\int_1^ \infty \frac {x^3+3}{x^6(x^2+1)} \, \mathrm d x=\frac{a+b\pi}{c}$, then find $a,b,c$.

24 votes
Accepted

What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?

10 votes
Accepted

Prove that $\sum_{n=1}^{\infty }\frac{B_{2n}}{(2n-1)!}=\frac{1}{2}-\frac{1}{(e-1)^2}$

8 votes

Solve $4 \times2^x+3^x=5^x$ without any sort of calculator

8 votes

All Invariant Subspaces of a Linear Transformation

8 votes
Accepted

What is intresting about $\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\cdots}}}}}}}}}=\log_x{e}$?

8 votes

Finding the expected value in the given problem.

6 votes
Accepted

Prove that $\sqrt{x}\sin\frac{\pi}{2\sqrt{x}}$ is not of bounded variation and is not Lipschitz

6 votes
Accepted

Proof $\dbinom{n}{0} - \frac{1}{2}\dbinom{n}{1} + \cdots + (-1)^n\frac{1}{2^{n-1}}\dbinom{n}{n-1}$

6 votes

Can we obtain $f(y+x)=y+f(x)$ from $f(x^2+f(x)^2+x)=f(x)^2+x^2+f(x)$?

6 votes
Accepted

Integrability of a function

5 votes
Accepted

Closed form solution for infinite summation

5 votes

Prove $\int_b^a [f(x)+f^{-1}(x)]dx=a^2-b^2$

5 votes
Accepted

How to find the radius of small inscribed circle?

5 votes
Accepted

Prove $\displaystyle \int_a^\infty f(x) \, dx \iff$ there exists $M_{\varepsilon}$

5 votes
Accepted

Two cards are drawn together from a pack of $52$ cards. What is the probability that one is spade and other is king?

5 votes

Reasoning Aptitude CSIR 15

5 votes
Accepted

Convolution of PDFs is a PDF

4 votes
Accepted

On a solution to a triple integral.

4 votes

If $\int_2^\infty f(x)^2 dx $ is convergent, is it true that $\int_2^\infty f(x)x^{-3/4} dx $ is convergent?

4 votes
Accepted

Solution $x^{73}+x^{48}+x^{26} \equiv 0$ mod $13$

4 votes

using AM-GM inequality to prove other inequalities

4 votes
Accepted

Test diagonalizability of $T(A)=A^t$ over all $n\times n$ matrices

4 votes

Finding $\lim_{x\to -2}{\frac{x+2}{\sqrt{-x-1}-1}}\;$ without L'Hospital

4 votes
Accepted

What is a non diagonal matrix?

4 votes
Accepted

Given $3$ types of coins, how many ways can one select $20$ coins so that no coin is selected more than $8$ times.

4 votes
Accepted

How many people are on the group?

4 votes
Accepted

Find the density of $Z=\frac{X}{Y}$ for an exponential distribution?

4 votes
Accepted

How many pairs are in $(B,C) \in P(A) \times P(A)$ such that $B \subseteq C$

4 votes
Accepted

Where am I wrong at deriving the formula of volume of cone?

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