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 Σ A


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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

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