Suppose a,b>0. Does the sequence {(a^n + b^n)^(1/n)} from n=1 to infinity converge? If so, find the limit.
Not sure where to start...
Factor out the larger of a and b. You'll need to consider the two cases where they're equal and not equal separately.
If the one case isn't clear to you, you could use the identity $\displaystyle p = e^{\ln(p)} \ \forall \ p>0$, and then look at the limit in the exponent.
Question:
$\displaystyle \text{If } \lim_{n \to \infty} q_n \text{ exists and equals } L, \text{ then } \lim_{n \to \infty} e^{q_n} = e^L \text{ is true because } $
$\displaystyle \text{ the function } f(x) = e^x \text{ is ?what? } $