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

Question

798 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-14T21:04:17

See below.

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

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

If P:RR->RRP:RR->RR verify this equality:P(1)+...+P(n)=n^5;n=1,2,...P(1)+...+P(n)=n^5;n=1,2,...,then how to find value of int_0^1P(x)dxint_0^1P(x)dx?