Thread: Sequence Limit

Show that if (z_n) = [(a^n + b^n)]^(1/n) where 0 < a < b, then lim(z_n) = b.

I see that b^n will obviously dominate as n goes to infinity, making it (b^n)^(1/n), but how do I show this with algebra or a theorem about sequences (can you use Squeeze Theorem easily?) ?

Originally Posted by jamesHADDY

Show that if (z_n) = [(a^n + b^n)]^(1/n) where 0 < a < b, then lim(z_n) = b.

I see that b^n will obviously dominate as n goes to infinity, making it (b^n)^(1/n), but how do I show this with algebra or a theorem about sequences (can you use Squeeze Theorem easily?) ?

and remember that .

--> use squeeze theorem.