Binomial Theorem

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 :