Binomial Theore...

Sum of the coefficients of $$ (1 - x)^{25} $$ is

The number of rational terms in the expansion of $$ \left ( \sqrt{3}+\sqrt[4]{5} \right )^{124} $$ is

$$ ^nC_0 + ^nC_2 + ^nC_4 + \dots \dots + ^nC_{2[n/2]} $$, where [ ] denotes greatest integer

If $$ (1+ax)^n = 1+9x+27x^2+ \dots \dots $$ then $$ (a, n) = $$

$$ \displaystyle \frac{^{15}C_1}{^{15}C_0}+2.\frac{^{15}C_2}{^{15}C_1}+3.\frac{^{15}C_3}{^{15}C_2}+\ldots+15.\frac{^{15}C_{15}}{^{15}C_{14}} = $$

$$ C_0^2+3.C_1^2+5.C_2^2 + \ldots\ldots +(2n+1).C_n^2 = $$

Sum of the coefficients in the expansion of $$ (5x-4y)^n $$ where $$n$$ is a positive integer is

If $$n$$ is a positive integer, then the coefficient of $$ x^n $$ in the expansion of $$ \dfrac{(1+2x)^n}{1-x} $$ is

$$ (1+x)^{15}=a_0+a_1x+\ldots\ldots+a_{15}x^{15} \Rightarrow \sum_{r=1}^{15}r\frac{a_r}{a_{r-1}}= $$

The sum of the coefficients in the expansion of $$ (1-x)^{10} $$