Summation problem to the fourth power
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Summation problem to the fourth power

[From: ] [author: ] [Date: 11-09-09] [Hit: ]
But I dont have a clue about something to the fourth power. Any help would be great thanks!!!!-0^4 + 1^4 + 2^4 + .......
The problem i have to solve is this.

Limit as N goes to infinity of 5/N(the summation from j=1 to N of (j/N)^4)... I think i can simplify that to 5/(N^5)(the summation from j=1 to N of j^4) ....

But then I don't know how to simplify it further. if it were j^3 i could rewrite the j^3 as (N^2(N+1)^2)/4

But I don't have a clue about something to the fourth power. Any help would be great thanks!!!!

-
0^4 + 1^4 + 2^4 + ... + n^4 = n(n+1)(2n+1)(3n^2+3n-1)/30

It can be found by assuming 1^4 + 2^4 + ... + n^4 = an^5 + bn^4 + cn^3 + dn^2 + en + f, letting n=0,1,2,3,4,5 and solving the linear equations.
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