" Ques-e - eracuate : "-{((1)/(3))^(-3)-((1)/(2))^(-3)}-:((1)/(4))^(-3)

3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. =

3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. =

e^(2((1)/(3)+(1)/(3)*(1)/(3^(3))+(1)/(5)*(1)/(3^(5))+….))=

e^(2((1)/(3)+(1)/(3)*(1)/(3^(3))+(1)/(5)*(1)/(3^(5))+….))=

(1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=

e^(x-1-(1)/(2)(x-1)^(2)+(1)/(3)(x-1)^(3)-(1)/(4)(x-1)^(4))+... =

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

I:2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...]=log_(e)2 II:2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=log_(e)2

The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to