Thread: show that lim(a^n+b^n)^(1/n) = b if 0<a<b

lim(a^n+b^n)^(1/n) = b if 0<a<b

i don't even know what to say. lost.

*edit*

ok got an idea: i know that (a^n+b^n)^(1/n) < (b^n+b^n)^(1/n) = 2^(1/n)*b, which converges to b

i'm thinking of using the squeeze theorem, i just need to find a lower bound that converges to b..

*edit*

found it: (b^n)^(1/n) < (a^n+b^n)^(1/n)

sorry for spamming... i gotta remember the motto: everything you need is in the problem.

but since .