`sum_(x=1)^n (-1)^(x-1) C(n,r)(a-r)=`

The value of sum_(x=1)^(n)(-1)^(r+1)(C(n,r))/(r+1) is equal to

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

Statement-1: sum_(r=0)^(n) (1)/(r+1) ""^(n)C_(r) = (1)/((n+1)x) {( 1 + x)^(n+1) -1}^(-1) Statement-2: sum_(r=0)^(n) (""^(n)C_(r))/(r+1) = (2^(n+1))/(n+1) .

Statement-1: sum_(r=0)^(n) (1)/(r+1) ""^(n)C_(r) = (1)/((n+1)x) {( 1 + x)^(n+1) -1}^(-1) Statement-2: sum_(r=0)^(n) (""^(n)C_(r))/(r+1) = (2^(n+1))/(n+1) .

(1+x)(sum_(r=0)^(n)nC_(r)x^(r))+(1+x^(2))(sum_(r=0)^(n-1)(n-1)C_(r)x^(r))+...(1+x^(n))(sum_(r=0)^(1)1C_(r)x^(r))=a_(0)+a_(1)x+, then the value of (a_(1))/(a_(n)+1)+(a_(1))/(a_(n))+(a_(2))/(a_(n-1))+......+(a_(n+1))/(a_(0)) is equal to

By method of induction, prove that sum_(r=1)^n ax^(r-1) = a ((1-x^n)/(1-x)) , for all n in N , x != 1 .