Ankit Kumar's user avatar
Ankit Kumar's user avatar
Ankit Kumar's user avatar
Ankit Kumar
  • Member for 5 years, 7 months
  • Last seen more than a month ago
10 votes

How can I prove that $\frac{e^x+e^y}{2}>e^\frac{x+y}{2}$, where $x \neq y$?

7 votes
Accepted

How to prove $\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\ldots}}}}}}=\frac {\sqrt {4a-3}-1}2$

6 votes
Accepted

Show that $S_n=1+{x\over1!}+{x^2\over2!}+\cdots+{x^n\over n!}$ converges for $n\in\Bbb N,\ x \in\Bbb R$ without using Taylor series.

4 votes
Accepted

Explain the process of solving this nested squareroot problem

4 votes
Accepted

Help understanding the steps of a solved limit

4 votes
Accepted

Odd Pythagorian triplets

3 votes

An order relation on the real numbers

3 votes

Let $f(x) = \ln x - 5x$, for $x > 0$.

3 votes

Find all complex numbers $z$ such that $\frac{6z^4 + 5z^2 + 6}{3z^4 + 10z^2 + 3}$ is a real number.

2 votes
Accepted

Substitution for integrals two different cases.

2 votes
Accepted

Prove: $\lim\limits_{x\to\infty}\left(\sin^2\left(\frac{1}{x}\right)+\cos\frac1x\right)^{x^{2}}=\sqrt{e}$

2 votes
Accepted

Number of numbers - P&C

2 votes
Accepted

Find the maximum value of $x+(p/x)$, if $x<0$ and $p>0$

2 votes
Accepted

Solving Generating Function when there is condition on two variables.

2 votes

least value of floor of $z_{1}+z_{2}$

2 votes
Accepted

Proof by induction: $\sum_{i=1}^{2^n} \frac{1}{2i-1} > \frac{n+3}{4}$ [SOLVED]

2 votes

Taylor's series formula for $\sin i$

2 votes
Accepted

Neural Network with Inner Loop

2 votes

Suppose a graph $G$ is connected with $n$ vertices and $e$ edges. If $n \geq 3$ and $G$ has exactly one cycle, prove that $e=n$.

2 votes

Writing $\frac{1}{(1+ixy)^{2n+1}} +\frac{1}{(1-ixy)^{2n+1}}$ in a way that is independent of $i$.

2 votes
Accepted

Conditional probabilities summing to one

2 votes

$u_{n+1} = a u_n +b u_{n-1} +c$

2 votes

Which type of triangle has the largest circularity value, $\sqrt{\frac{4\pi\cdot\text{area}}{\text{perimeter}^2}}$?

1 vote

Condition that the line $y=mx+c$ is normal to a conic

1 vote
Accepted

AMC 1834 - If $a, b $ and $c$ are nonzero numbers such that (a+b-c)/c=(a-b+c)/b=(-a+b+c)/a and x=((a+b)(b+c)(c+a))/abc and x<0, then x=?

1 vote
Accepted

A lower bound for the number of triangles that contain a particular edge

1 vote

A proving question based on greatest integer function.

1 vote
Accepted

Is there a graph of 40 vertices of grade 1 to 40?

1 vote

Strength of salt in a mixture is p%. Various concentration of slats are added

1 vote

Find asymptotic upper bound of Pascal Triangle