Show that sq. root of 2 to power sq. root of 2 to N converges

[sigdel977]

Show that sq. root of 2 to power sq. root of 2 to ... N converges

Sq. root of 2^sq root of 2 ^ sq. of 2...N
Use monotonous convergence theorem to that it converges and determine what it converges to.

 

[Dick]

Your definition of the sequence is ambiguous. Do you mean a_n+1=a_n^sqrt(2) or a_n+1=sqrt(2)^a_n? Try punching out some terms on a calculator of each. One of them doesn't converge. Then tell me what you need to prove about the sequence to use the monotone convergence theorem.

 

[sigdel977]

i ment,
(sq. rt of 2)^(sq. rt of 2)^(sq. rt of 2)^N

 

[Dick]

i ment,
(sq. rt of 2)^(sq. rt of 2)^(sq. rt of 2)^N

sqrt(2)^sqrt(2)^sqrt(2) doesn't mean anything. (sqrt(2)^sqrt(2))^sqrt(2) and sqrt(2)^(sqrt(2)^sqrt(2)) are different. Use parentheses. It's easier if you define a_n+1 in terms of a_n.