MathGroup Archive 2004

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limits


hello all,
Would you please help me in any of these limits:
Prove:
lim(1^p+2^p+3^p+...+n^p)/n^(p+1)= 1/(p+1)
n->infinity

lim(1^p+2^p+3^p+...+n^p- n/(1+p))= 0.5
n->infinity

lim(1/n)(1+1/2+1/3+...+1/n)=0
n->infinity


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