let give a sequence of reals (a_n )_n / a_n >0 and U_n = (a_n /((1+a_1 )(1+a_2 )....(1+a_n ))) 1) prove that Σ u_n converges 2) calculate Σ u_n if u


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Question Number 28617 by abdo imad last updated on 27/Jan/18

$l e t g i v e a s e q u e n c e o f r e a l s {(a_{n})}_{n} / a_{n} > 0 a n d$ $U_{n} = \frac{a_{n}}{(1 + a_{1}) (1 + a_{2}) . . . . (1 + a_{n})}$ $1) p r o v e t h a t Σ u_{n} c o n v e r g e s$ $2) c a l c u l a t e Σ u_{n} i f u_{n} = \frac{1}{\sqrt{n}} .$
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