lim_(n->oo)(9*9^(1/3)*9^(1/9)*9^(1/27)*......*9^(1/(3^n)) ?

1 Answer
Feb 19, 2018

27

Explanation:

prod_(k=0)^oo 9^(1/(3^k)) = 9^(sum_(k=0)^oo 1/3^k)

and

sum_(k=0)^oo 1/3^k = 1/(1-1/3) = 3/2 hence

prod_(k=0)^oo 9^(1/(3^k)) = 9^(3/2) = 27