Determinare il termine generale delle seguenti successioni:

a) $\displaystyle \frac{1}{2},\: \frac{2}{3},\:\frac{3}{4},\:\frac{4}{5},\:\frac{5}{6},\ldots$

$\displaystyle a_n=\frac{n}{n+1},\:n\in \mathbb{N}, n\geq 1$

b) $\displaystyle 1,\: \frac{1}{3},\: \frac{1}{9},\:\frac{1}{81},\ldots$

$\displaystyle a_n=\frac{1}{3^n},\:n\in \mathbb{N}$

c) $\displaystyle -2,\: 4,\: -8,\:16,\ldots$

$\displaystyle a_n= (-1)^n\cdot 2^n,\:n\in \mathbb{N}, n\geq 1 $