Combinatorial identities of the following sums

Question

Let $n > 1$ be some natural number. I am looking for a closed-form expression for the following sums (they seem very natural, so I guess this is well-known):

$1+2^{n-1}+3^{n-2}+...+n$

$2^n+2 \cdot 3^{n-1} +...+ n(n+1)$