Evaluate the limits.

2011-08-08 6:00 am
Let p >= 2 and
a=lim(n→∞) [ (1^p+2^p+3^p+...+n^p)/n^(p+1) ]
b=lim(n→∞) [ (1^p+2^p+3^p+...+n^p)/n^p - an ]
c=lim(n→∞) [ (1^p+2^p+3^p+...+n^p)/n^(p-1) - an² - bn ],
find a, b and c =?

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更新1:

In fact, it is sufficient for any constants p > 1 (not necessarily for integer p).

回答 (3)

2011-08-09 3:13 am
1. 1/(p+1)
2. 1/2
3. p/12


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