Are you familiar with the exponential series, expansion of ?Originally Posted by Nichelle14
KeepSmiling
Malay
It's been awhile since I have done these types of problems.
Can the sum of a series have a factorial in the answer?
this is my problem: Summation of (n/(n+1)!) with n>= 1
while working it out, I found that this is 1/(n+1)(n-1)!
can that be an answer?
Consider a function,
Its derivative is, (since it is absolutely convergent)
Thus, (since it is abolsulte convegent)
Now, (as malaygoel said) are you familiar with,
Then you are left with,
Thus, to solve this diffrencial equation find,
use integration by parts with,
then, and thus, .
Thus, (by parts)
Thus,
we see that,
Thus,
thus,
Finally our required function is,
Note, the infinite sum, as you said,
Is, the same as which in this case is,