[" Sum to "(n+1)" terms of the series "],[(C_(0))/(2)-(C_(1))/(3)+(C_(2))/(4)-(C_(3))/(5)+......" is "]

The sum to (n+1) terms of the series (C_(0))/(2)-(C_(1))/(3)+(C_(2))/(4)-(C_(3))/(5)+......=

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , find the sum of the series (C_(0))/(2) -(C_(1))/(6) + (C_(2))/(10) + (C_(3))/(14) -...+ (-1)^(n) (C_(n))/(4n+2) .

If C_(r) stands for nC_(r), then the sum of first (n+1) terms of the series aC_(0)-(a+d)C_(1)+(a+2d)C_(2)-(a+3d)C_(3)+...... is

The sum to (n+1) terms of the series C_0/2-C_1/3+C_2/4-C_3/5+......=

(C_(0))/(1*2)+(C_(1))/(2*3)+(C_(2))/(3*4)+...+(C_(n))/((n+1)(n+2))=

(C_(0))/(1.2)+(C_(1))/(2.3)+(C_(2))/(3.4)+......*(C_(n))/((n+1)(n+2))=

If C_(0),C_(1),C_(2),...,C_(n) denote the binomial coefficientsin the expansion of (1+x)^(n), then (C_(0))/(2)-(C_(1))/(3)+(C_(2))/(4)-(C_(3))/(5)+......+(-1)^(n)(C_(n))/(n+2)=