Binomial Theore...

If $$n$$ is a positive integer, then the coefficient of $$ x^n $$ in the expansion of $$ \dfrac{(1+x)^n}{1-x} $$ is

$$ ^5C_0+2.^5C_1+2^2.^5C_2+2^3.^5C_3 +2^4.^5C_4+2^5.^5C_5 = $$

If $$ n\geq2 $$ then $$ (a-1).C_1-(a-2).C_2+(a-3).C_3-\ldots\ldots(-1)^{n-1}(a-n).C_n= $$

If $$a$$ is the coefficient of the middle term in the expansion of $$(1+x)^{2n}$$ and $$b, c$$ are the coefficients of the two middle terms in the expansion of $$(1+x)^{2n-1}$$ then 

The number of rational terms in the expansion of  $$(1+\sqrt{2}+\sqrt[3]{3})^{6}$$ is

Coefficient of $$x$$ in the expansion of $$(1-2\displaystyle {x}^{3}+3{x}^{5})(1+\frac{1}{{x}})^{8}$$ is

The coefficient of $$\displaystyle \frac{1}{{x}}$$ in the expansion of $$(1+\displaystyle x)^{{n}}(1+\frac{1}{{x}})^{{n}}$$ is :

The middle term in the expansion of $$(1-3{x}+3{x}^{2}-{x}^{3})^{2{n}}$$ is

The coefficient of $${x}^{p}$$ the expansion of $$(\displaystyle {x}^{2}+\frac{1}{{x}})^{{n}}$$, when it exists is