16. Prove that `x^n/n!+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^2)/((n-2)!2!).....+a^n/(n!)=(x+a)^n/(n!)`

Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2)!2!)+(x^(n-3).a^(3))/((n-3)!3!)+.......(a^(n))/(n!)=(x+a)^(n)/(n!)

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2 tan^(-1)x^n

n + (n-1) x + (n-2) x ^ (2) + ....... + 2x ^ (n-2) + x ^ (n-1)

(d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Find the value of (1+x)^(n)+^(n)C_(1)(1+x)^(n-1).(1-x)+^(n)C_(2)(1+x)^(n-2)(1-x)^(2)+.....+(1-x)^(n)

Divide x^(2n)+a^(2^(n-1))x^(2^(n-1))+a^(2^(n))byx^(2^(n-1))-a^(2^(n-2))x^(2^(n-2))+a^(2^(n-1))

The coefficient of 1/x in the expansion of (1+x)^(n)(1+1/x)^(n) is (n!)/((n-1)!(n+1)!) b.((2n)!)/((n-1)!(n+1)!) c.((2n-1)!(2n+1)!)/((2n-1)!(2n+1)!) d.none of these