Thread: Prove result for binomial coefficients?

1. Prove result for binomial coefficients?

Prove that:

$\left(\sqrt{n\choose 1} + \sqrt{n\choose 2} + \mbox{...} + \sqrt{n\choose n}\right)^2 \leq n\cdot (2^n - 1)$.

2. Use the Cauchy–Schwarz inequality.