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  • Member for 9 years, 8 months
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  • India
29 votes

To Find Eigenvalues

26 votes
Accepted

If $\sum (a_n)^2$ converges and $\sum (b_n)^2$ converges, does $\sum (a_n)(b_n)$ converge?

24 votes
Accepted

To Find Eigenvalues

13 votes
Accepted

Evaluate the limit $\lim_{n\to\infty} \frac{3^n}{2^n+3^n} $

12 votes

Evaluate the integration : $\int\sqrt{\frac{(1-\sin x)(2-\sin x)}{(1+\sin x)(2+\sin x)}}dx$

11 votes
Accepted

A function not differentiable exactly two points of $[0,1]$. construction of such a function is possible?

10 votes
Accepted

$\sum_{n=1}^\infty \dfrac {2n+1}{n^2(n+1)^2} = ?$

10 votes

A supposed to be easy calculus problem

10 votes

How to check the set to be closed?

10 votes
Accepted

Evaluate the limit $\lim_{x\to \infty}( \sqrt{4x^2+x}-2x)$

9 votes
Accepted

Convergence of $\sum_{n=1}^\infty (\frac{n}{n+1})^{n^2}$

8 votes
Accepted

Show that $O(n)$, the set of orthogonal $n \times n$ matrices, is not connected

7 votes
Accepted

To evaluate $\lim_{n \to \infty} \left(1+\frac{1}{2n}\right)^{n+5}$

7 votes

Is there another simple way to solve this integral $I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$?

6 votes

Is the closure of $\mathbb Q \times \mathbb Q$ equal to $\mathbb R \times \mathbb R$?

6 votes

How many elements are in the quotient ring $\frac{\mathbb Z_3[x]}{\langle 2x^3+ x+1\rangle} $

6 votes
Accepted

Examine the convergence of $\sum_{n=1}^\infty \frac1{n(\log_2n)}$

6 votes
Accepted

Given $x\in \left(0; \frac\pi2\right)$. Prove that $\sin x>\frac{2x}{\pi}$

6 votes

Let $a_n$ and $b_n$ be two sequences of real numbers such that series $a_n^2$ and $b_n^2$ converge. Then the series $a_nb_n$

6 votes

Easiest way to show sequence $e^{\frac{1}{n}}$ converges to 1

5 votes

Find limits of sequences

5 votes

problem on existence of entire function

5 votes
Accepted

Number of Zeros in the Right Half Plane

5 votes

Exact Differential Equations $(axy^2+by)dx+(bx^2y+ax)dy=0$.

5 votes
Accepted

If an entire function $f$ satisfying $f(i) = f(-i) = f(1) = f(-1) = f(i + 1) = 0$ show that $f\equiv 0$

5 votes
Accepted

$S_2=\sum_{n=1}^\infty \dfrac {(-1)^{n-1} (2n+1) } {n(n+1)} = ?$

5 votes

For a non-constant entire function which property is possible?

5 votes
Accepted

Remainder of $37^{100}\equiv \pmod {29}$

4 votes
Accepted

$\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital

4 votes

Linear Algebra minimal Polynomial

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