SOLUTION: Find the sum of the series 1+(1+a)/2!+(1+a+a^2)/3!+....infinity

Question 1089120: Find the sum of the series
1+(1+a)/2!+(1+a+a^2)/3!+....infinity

Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
.

Let S = 1+(1+a)/2!+(1+a+a^2)/3!+....infinity


Multiply all and every terms/term by (1-a). You will get

(1-a)*S =  +  +  + . . . = 

        =  - ( +  +  + . . .) = 

        =  -  = .


Hence,  S = , under the condition a =/= 1.


        At a = 1, then the sum S = 1 + e.

Solved.

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