Find the coefficient of ${x^9}$ in the expansion of $ (1 + x)( 1 + x^2)( 1 + x^3)..(1 + x^{100})$
128496
Find the coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3)...(1+x^{100})$
114418
A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
78632
Summation equation for $2^{x-1}$
9610
Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
156545
Find undetermined coefficients in polynomial quotient and remainder
33105
Find the value of $a^2-b^2+c^2$
116795
Easiest way to extract the coefficient of a polynomial
157552
Find the coefficient of $x^n$ simply by using binomial theorem
64592
The last two digits of $9^{9^9}$
49744
Find remainder of division of $x^3$ by $x^2-x+1$
138756
How to Calculate the Sum of Coefficients in a Polynomial with known Integer Roots
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
17333
Definite Integral $\int_2^4\frac{\sqrt{\log(9-x)}}{\sqrt{\log(9-x)}+\sqrt{\log(3+x)}}dx$
31122
How could I find $x$ in this equation $x^2-x+6 \equiv 0 \pmod {9}$
132610
Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)
137027
Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
110955
Find the coefficient of $x^9$ in $(1+x)(1+x^2)(1+x^3)\cdots(1+x^{100})$