Find the coefficient of $x^{9\ }$ in$\left(1+x\right)\left(1+x^{2}\right)\left(1+x^{3}\right)...\left(1+x^{100}\right)$
61047
Find the coefficient of ${x^9}$ in the expansion of $ (1 + x)( 1 + x^2)( 1 + x^3)..(1 + x^{100})$
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
64800
Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
139215
Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
128496
Find the coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3)...(1+x^{100})$
155527
Find coefficient for $x^{10}$ in $x^3(x^2-3x^3-1)^6$
87907
How to find the maximum and minimum value of $\left|(z_1-z_2)^2 + (z_2-z_3)^2 + (z_3-z_1)^2\right|$ (where $|z_1|=|z_2|=|z_3|=1$)?
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
913
Evaluating $\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$
146753
Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
22948
Is this binomial coefficient identity known?
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
136066
Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
96875
Finding the value of $x^{x^2}+x^{x^6}$ given that $x^{x^4}=4$
155353
Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$
33392
Proving that $ \ln\left(\frac{49}{50}\right)<\sum^{98}_{k=1}\int^{k+1}_{k}\frac{k+1}{x(x+1)}dx<\ln(99)$
156545
Find undetermined coefficients in polynomial quotient and remainder