If #P:RR->RR# verify this equality:#P(1)+...+P(n)=n^5;n=1,2,...#,then how to find value of #int_0^1P(x)dx#?

1 Answer
Cesareo R.
May 14, 2017

See below.

Explanation:

Considering that the problem is:

#P(1/n)+P(2/n)+ cdots+P(k/n)+ cdots+P((n-1)/n) + P(1) = n^5#

In this case we have

#lim_(n->oo)sum_(k=1)^n (P(k/n))/n = int_0^1P(xi) d xi = lim_(n->oo)n^4=oo^4=oo#

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