Partial sum of a series (help!)

  • Thread starter Feynmanfan
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  • #1
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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
 

Answers and Replies

  • #2
HallsofIvy
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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
[tex]\Sigma_{i=1}^n i^{1+\frac{1}{i}} [/tex].

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

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

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