1-prove-that-if-f-is-decreasing-function-we-have-n-n-1-f-t-dt-lt-f-n-lt-n-1-n-f-t-dt-2-let-put-S-n-k-1-n-2-1-2-k-calculate-S-n-

Question Number 30484 by abdo imad last updated on 22/Feb/18

1) p r o v e t h a t i f f i s d e c r e a s i n g f u n c t i o n w e h a v e

\int_{n}^{n + 1} f (t) d t < f (n) < \int_{n - 1}^{n} f (t) d t .

2) l e t p u t S_{n} = \sum_{k = 1}^{n^{2}} \frac{1}{2 \sqrt{k}} . c a l c u l a t e [S_{n}] .