# Induction Proof

• April 6th 2010, 11:28 AM
BlackBlaze
Induction Proof
Prove that $2^{\frac{1}{n}} <= 1 + \frac{1}{n}$.
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.

• April 6th 2010, 12:42 PM
Drexel28
Quote:

Originally Posted by BlackBlaze
Prove that $2^{\frac{1}{n}} <= 1 + \frac{1}{n}$.
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.

$2^{\frac{1}{n}}\leqslant 1+\frac{1}{n}\Leftrightarrow 2\leqslant\left(1+\frac{1}{n}\right)^n$. That's easier to work with.