let-give-a-sequence-of-reals-a-n-n-a-n-gt-0-and-U-n-a-n-1-a-1-1-a-2-1-a-n-1-prove-that-u-n-converges-2-calculate-u-n-if-u-n-1-n-

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}) \dots . (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}} .