### Binomial Theorem

goals
If $(x-2)^{100} = \sum_{r=0}^{100}a_r.x^r$, then
$a_1+2a_{2}.........+100a_{100}=$
The co-efficient of $\displaystyle x^{401}$ in the expansion of $\displaystyle \left ( 1+x+x^{2}+\cdot \cdot \cdot +x^{9} \right )^{-1}$ $\displaystyle \left ( \left | x \right |< 1 \right )$ is
The total number of terms in the expansion of $(x+y)^{50}+(x-y)^{50}$ is
What is the $r^{th}$ term in the expansion of a binomial $(x + y)^n$?
If $(2+\dfrac {x}{3})^{55}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive terms of the expansion are equal, then these terms are :