The exercise states: Does the series $$\sum\limits_{n=1}^\infty \int_{0}^1 \frac{x^n dx}{x+1}$$ converge?
The solution states as the first step: $$I_n =\int_{0}^1 \frac{x^n dx}{x+1} $$ then $ \frac{1}{2(n+1)}\le I_n \le \frac{1}{n+1} $
This is not really self evident to me, could someone explain where this inequality comes from to me?
Hint: $\dfrac{x^n}{0+1} \geq\dfrac{x^n}{x+1} \geq \dfrac{x^n}{1+1}$