mathematical-Analysis-if-n-0-1-x-2n-1-log-1-x-dx-then-find-the-value-of-n-1-1-n-n-m-n-

Question Number 143231 by mnjuly1970 last updated on 11/Jun/21

\dots . . m a t h e m a t i c a l \dots \dots A n a l y s i s \dots .

i f :: ϕ (n) := \int_{0}^{1} x^{2 n - 1} l o g (1 + x) d x

t h e n f i n d t h e v a l u e o f ::

Θ := \underset{n = 1}{\sum^{\infty}} {(- 1)}^{n} ϕ (n)

\dots \dots . m . n