Binomial Theore...

Find the middle terms(s) in the expansion of $$\left ( 3x-\dfrac{2}{x^{2}} \right )^{15}$$.

The value of $$\dfrac{1}{12!}+\dfrac{1}{10!2!}+\dfrac{1}{8!4!}+...+\dfrac{1}{12!}$$

Coefficient of $$x^{25}$$ in $$(1+x+x^{2}+x^{3}+....+x^{10})^{7}$$ is

The greatest terms of the expansion $$(2x+5y)^{13}$$ when $$x=10$$, $$y=2$$ is?

The coefficient of $$x^{8}$$ in $$(1+2x^{2}-x^{3})^{9}$$ is 

The coefficient of x$$^9$$ in (x - 1) (x - 4) (x - 9)........(x - 100) is

Find the value of $$\dfrac{1}{\left(n-1\right)!}+\dfrac{1}{\left(n-3\right)!3!}+\dfrac{1}{\left(n-5\right)!5!}+...$$

The constant term in the expansion of $${ (1+x) }^{ n }{ (1+\frac { 1 }{ x } ) }^{ n }$$ is 

The coefficient of $$x^{3}$$ in the expansion of $$(1+2x+3x^{2})^{10}$$ is

The largest coefficient in the expansion of $$\left(4+3x\right)^{25}$$ is