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, 04:07 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, 04:47 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 , and then look at the limit in the exponent.

Question:

- Oct 17th 2012, 05:10 PMPlatoRe: Convergent Sequence
- Oct 17th 2012, 05:23 PMlovesmathRe: Convergent Sequence
How did you get the 2 under the radical at the end of the inequality?

- Oct 17th 2012, 06:45 PMPlatoRe: Convergent Sequence