Skip to main content
choco_addicted's user avatar
choco_addicted's user avatar
choco_addicted's user avatar
choco_addicted
  • Member for 8 years, 2 months
  • Last seen more than 3 years ago
107 votes
Accepted

$100$-th derivative of the function $f(x)=e^{x}\cos(x)$

31 votes

Prove the following trigonometric identity without a calculator involved

18 votes
Accepted

How to calculate $ \sum_{n=1}^{15}n(n!) = ? $

14 votes

How to prove that $k^3+3k^2+2k$ is always divisible by $3$?

10 votes
Accepted

Find $3a+b+3c+4d$ if $\left(\begin{smallmatrix}-4&-15\\2&7\end{smallmatrix}\right)^{100}=\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)$.

9 votes
Accepted

how to prove that $2^n = (n+1)(n+2)(n+3)$ has no solution when $n>0$?

9 votes
Accepted

Decide whether the series ${\sum_{n=1}^{\infty} \frac{1+5^n}{1+6^n}}$ converges or diverges

9 votes
Accepted

Exponential (to the power of a logarithm)

8 votes
Accepted

Solve $e^{4z} +e^{3z} + e^{2z} + e^z + 1 = 0$.

8 votes
Accepted

Weight of watermelons after percentage of water is evaporated.

7 votes
Accepted

Let $P$ be a 4-th degree real polynomial with 5 conditions given. How to compute $P(4)$?

7 votes
Accepted

Find the value of $\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90}$

7 votes

Evaluate $\lim_{x \to 0} \frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x}$

7 votes

How would you solve this system if linear equations in 3 variables?

6 votes
Accepted

If $ \frac{x}{b-c} = \frac{y}{c-a} = \frac{z}{a-b}$, Prove that $x+y+z$ $=0$

6 votes

integrate $\cos(x)+\sqrt{1+x^2}\sin^3(x)\cos^3(x)$

6 votes
Accepted

Does $\sum_{n=1}^\infty {\frac{ \sin(\frac{n\pi}{6})}{\sqrt {n^4 + 1}}}$ converge?

6 votes
Accepted

Proof that $\sum_{i=0}^n 2^i = 2^{n+1} - 1$

6 votes

Recovering a quadratic polynomial from three values using calculus

6 votes

Compute $\sum\limits_{n=1}^{\infty} \frac1{1+x_n}$ if $x_1>0$ and $ x_{n+1} = x_n ^2 + x_n $

6 votes

Is $x^4 + 4$ irreducible in $\mathbb{Z}_5$?

6 votes

Why $\sum_{n=1}^\infty {\ln(n^2) \over n^2 }$ converges?

6 votes
Accepted

Find $a^{100}+b^{100}+ab$

6 votes

Discuss the differentiability of $e^{-|x|}$?

5 votes
Accepted

Show $\int_{0}^{1} \sin(x+\frac{1}{x})dx$ converges.

5 votes
Accepted

What is $i^i$ and $(i^i)^i$

5 votes

Determine whether or not the following series are convergent $\sum_{n=1}^\infty n\sin(\frac{1}{n})$

5 votes

Real solution of the equation $\sqrt{a+\sqrt{a-x}} = x\;,$ If $a>0$

5 votes

Evaluate $\lim_{n\to\ \infty} \frac{3^{n+1} + 2^{n+2}}{3^{n-1} + 2^{n-2}} $

5 votes
Accepted

indefinite integration $ \int \frac { x^2 dx} {x^4 + x^2 -2}$

1
2 3 4 5
9