# Partial sum of a series (help!)

1. Apr 25, 2004

### Feynmanfan

Hello everybody!

I'm having some trouble with series. My calculus teacher asked us to find the partial sum of

Sigma from 1 to n [n^-(1 + 1/n)]

It is obvious that the series diverges when trying to find the infinite sum. However, is it possible to find an expression dependant of n of the partial sum? I don't know where to start from

2. Apr 25, 2004

### HallsofIvy

Staff Emeritus
Well, one problem you have is that your problem doesn't make sense.

You shouldn't use "n" for both the upper limit of summation and as the index inside the sum.

I assume that what you really mean is
$$\Sigma_{i=1}^n i^{1+\frac{1}{i}}$$.

There is no simple formula so you can't just plug a number in.

I recommend that you try some values of n and see what happens:

If n= 1, the sum is simply $1^{1+1}= 1$
If n= 2, the sum is $1+ 2^{1+1/2}= 1+ 2\sqrt{2}$
If n= 3, the sum is $1+ 2\sqrt{2}+ 3^{1+ 1/3}= 1+ 2\sqrt{2}+ 3(3)^{\frac{1}{3}}$

I see a pattern but I don't see any simple way of writing that.