+((-1)^(n-1))/(n)C_(n)=1+(1)/(2)+(1)/(3)+cdots+(1)/(n)

Prove that (C_(1))/(1)-(C_(2))/(2)+(C_(3))/(3)-(C_(4))/(4)+...+((-1)^(n-1))/(n)C_(n)=1+(1)/(2)+(1)/(3)+...+(1)/(n)

If H_(n) =1+(1)/(2)+ cdots + (1)/(n) then value of S_(n) =1 + (3)/(2) + (5)/(3) +cdots + (2n-1)/(n) is

1^(2)C_(1)-2^(2)C_(2)+3^(2)C_(3)-+(-1)^(n-1)n^(2)C_(n)=(1)(n^(2)*2^(n+1))/(n+1)(3)(2^(n+1))/(n-1)

(1+ (C_1)/(C_0)) (1+(C_2)/(C_3) )....(1+(C_n)/(C_(n-1))) is equal to : a) (n+1)/(n!) b) ((n+1)^(n))/((n-1)!) c) ((n-1)^(n))/(n!) d) ((n+1)^(n))/(n!)

For a positive integer n let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)cdots+(1)/((2^(n))-1). Then a(100) 100c.a(200)<=100d.a(200)<=100

If S_(1), S_(2),cdots S_(n) , ., are the sums of infinite geometric series whose first terms are 1, 2, 3,…… ,n and common ratios are (1)/(2) ,(1)/(3),(1)/(4),cdots,(1)/(n+1) then S_(1)+S_(2)+S_(3)+cdots+S_(n) =

Prove that C_(0)-(1)/(3)*C_(1)+(1)/(5)*C_(2) - …+(-1)^(n)*(1)/(2n+1)C_(n) =(2^(2n)(n !)^(2))/((2n+1)!)

Find .^(n)C_(1)-(1)/(2).^(n)C_(2)+(1)/(3).^(n)C_(3)- . . . +(-1)^(n-1)(1)/(n).^(n)C_(n)

Find .^(n)C_(1)-(1)/(2).^(n)C_(2)+(1)/(3).^(n)C_(3)- . . . +(-1)^(n-1)(1)/(n).^(n)C_(n)

Statement-1: (C_(0))/(2.3)- (C_(1))/(3.4) +(C_(2))/(4.5)-.............+............+(-1)^(n) (C_(n))/((n+2)(n+3))= (1)/((n+1)(n+2)) Statement-2: (C_(0))/(k)- (C_(1))/(k+1) +(C_(2))/(k+3)+............+(-1)^(n) (C_(n))/(k+n)=int_(0)^(1)x^(k-1) (1 - x)^(n) dx