Question

Given {\[{{a_n}}\]} is decrease and positive, and
series \[\sum\limits_{n = 1}^\infty {{{\left( { - 1} \right)}^n}{a_n}} \]
is divergent.
set \[{u_n} = (\frac{1}
{{1 + {a_1}}})(\frac{1}
{{1 + {a_2}}})...(\frac{1}
{{1 + {a_n}}})\]
Question: the series \[\sum\limits_{n = 1}^\infty {{u_n}} \]
is divergent or convergent, and why.

Answer 1

Please somebody help... I am desperate..