Prove that $\displaystyle 2^{\frac{1}{n}} <= 1 + \frac{1}{n}$.

for n in the set of all positive numbers.

Base case is obvious.

So, tried using n = k, and adding k+1.

But then I get a load of terms and it gets too messy to handle.

Any advice?

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- Apr 6th 2010, 11:28 AMBlackBlazeInduction Proof
Prove that $\displaystyle 2^{\frac{1}{n}} <= 1 + \frac{1}{n}$.

for n in the set of all positive numbers.

Base case is obvious.

So, tried using n = k, and adding k+1.

But then I get a load of terms and it gets too messy to handle.

Any advice? - Apr 6th 2010, 12:42 PMDrexel28