Thread: sum of a series

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?

Originally Posted by Nichelle14

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?

Are you familiar with the exponential series, expansion of ?

KeepSmiling
Malay

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,

I vaguely remember the exponential series of e^x.

I was able to follow your work though.

This may be a silly question but what exactly is the answer? Do I need to do more?

Also, when you were trying to find C, why did you set the function equal to 1?

Originally Posted by Nichelle14

I vaguely remember the exponential series of e^x.

I was able to follow your work though.

This may be a silly question but what exactly is the answer?

2, because that series as I explained is .

Also, when you were trying to find C, why did you set the function equal to 1?

My error. You are right.
I editted my post.