Review question

# Can we find an inequality from the expansion of $[ 1+1/\sqrt{n}]^n$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6770

## Question

By considering the first three terms of the binomial expansion of $\left[ 1+\left(\dfrac{1}{\sqrt{n}}\right) \right]^n$, where $n$ is an integer greater than $1$, prove that $\left[1+\left(\frac{1}{\sqrt{n}}\right)\right]^{n-2} \geq \tfrac{1}{2}n.$