The sum of the series `1/(2!)-1/(3!)+1/(4!)-...` upto infinity is (1) `e^(-2)` (2) `e^(-1)` (3) `e^(-1//2)` (4) `e^(1//2)`

The sum of the series (1)/(1*2)-(1)/(2*3)+(1)/(3*4)--- upto oo is equal to

The sum of the series 1+2x+3x^(2)+4x^(3)+... upto infinity when x lies between 0 and 1 i.e.,0

The sum of the series (1^(2))/(2!)+(2^(2))/(3!)+(3^(2))/(4!)+ is e+1 b.e-1 c.2e+1 d.2e-1

The sum of the series 1+1/4.2!1/16.4!+1/64.6!+………to oo is (A) (e+1)/(2sqrt(e)) (B) (e-1)/sqrt(e) (C) (e-1)/(2sqrt(e)) (D) (e+1)/2sqrt(e)

Find the sum of the series e^(x-(1)/(2)(x -1)^(2) + (1)/(3) (x -1)^(3) - (1)/(4) (x -1)^(4) + ...

Statement -1: The sum of the series (1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)+..to infty is e Statement 2: The sum of the seies (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(4)/(4!)x^(4)..to infty is x e^(x)

Sum of the infinite series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+...to oo(e)/(3) b.e c.(e)/(2)d . none of these

Prove that, 1/(1.2)-1/(2.3)+1/(3.4)-.....=2log_e2-1

The sum to infinity of the following series (1)/(1*2)+(1)/(2*3)+(1)/(3*4)+.... shall be

Show tha, 1+1/(2!)+1/(4!)+....=1/2(e+1/e)