Can someone help me with this problem:

lim (n^2 + n)^(1/n) = 1;

In (b) you may assume that n^1/n = 1.

I know how to solve these when it's a number to the power of n but not when it's n to a power.

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- May 5th 2010, 10:46 AMMathsnewbieLimits
Can someone help me with this problem:

lim (n^2 + n)^(1/n) = 1;

In (b) you may assume that n^1/n = 1.

I know how to solve these when it's a number to the power of n but not when it's n to a power. - May 5th 2010, 11:22 AMJG89
$\displaystyle (n^2 + n)^{1/n} = [n(n+1)]^{1/n} = n^{1/n} (n+1)^{1/n} $.

Can you show that $\displaystyle (n+1)^{1/n} $ goes to 1 as n goes to infinity? - May 5th 2010, 11:24 AMtonio
- May 5th 2010, 11:25 AMMathsnewbie
- May 5th 2010, 11:28 AMtonio
- May 5th 2010, 11:34 AMMathsnewbie
Thank you, I managed to complete (Evilgrin)