let-A-n-n-n-x-1-x-x-dx-with-n-natural-integr-and-n-1-1-find-A-n-interms-of-n-2-find-nature-of-the-serie-A-n-

Question Number 57194 by maxmathsup by imad last updated on 31/Mar/19

l e t A_{n} = \int_{n}^{n} \frac{[\sqrt{x + 1}] - [\sqrt{x}]}{x} d x w i t h n n a t u r a l i n t e g r a n d n ⩾ 1

1) f i n d A_{n} i n t e r m s o f n

2) f i n d n a t u r e o f t h e s e r i e Σ A_{n}

Commented by maxmathsup by imad last updated on 31/Mar/19

A_{n} = \int_{1}^{n} \frac{[\sqrt{x + 1}] - [\sqrt{x}]}{x} d x