# How to show that \$sum_{i=1}^n 1-e^{-n p^i/i} = Omega(log n)\$ for \$0 < p < 1/2\$?

Let $$0 < p < 1/2$$. How can I show the following lower bound?

$$sum_{i=1}^n 1-expleft(- frac{np^i}{i}right) = Omega(log n)$$