Two Telescoping Bounds

Let $a_n = n(n+1)\cdot 2^n$ for $n \in \mathbb{N}^*$. Prove:

1. $\dfrac{3}{a_1} + \dfrac{4}{a_2} + \cdots + \dfrac{n+2}{a_n} < 1$; 2. $\dfrac{4}{a_1} + \dfrac{5}{a_2} + \cdots + \dfrac{n+3}{a_n} < \dfrac{4}{3}$.