advanced-calculus-p-q-are-positive-integers-and-p-q-let-p-q-0-1-x-p-1-x-q-dx-prove-that-n-n-1-1-n-1-k-1-n-k-1-

Question Number 124102 by mnjuly1970 last updated on 30/Nov/20

\dots a d v a n c e d c a l c u l u s \dots

p, q a r e p o s i t i v e i n t e g e r s a n d

p ⩾ q : l e t : ϕ (p, q) = \int_{0}^{1} x^{p} {\frac{1}{x}}^{q} d x

p r o v e t h a t ::

ϕ (n, n) \overset{?}{=} 1 - \frac{1}{n + 1} \underset{k = 1}{\sum^{n}} ζ (k + 1)