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...

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- Oct 17th 2012, 03:07 PMlovesmathConvergent Sequence
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... - Oct 17th 2012, 03:47 PMjohnsomeoneRe: Convergent Sequence
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? } $ - Oct 17th 2012, 04:10 PMPlatoRe: Convergent Sequence
- Oct 17th 2012, 04:23 PMlovesmathRe: Convergent Sequence
How did you get the 2 under the radical at the end of the inequality?

- Oct 17th 2012, 05:45 PMPlatoRe: Convergent Sequence