\(\sum _{j=0}^{n+1} q^j = \sum _{j=0}^{n} q^j + q^{n+1} = \frac{1-q^{n+1}}{1-q} + q^{n+1}= \frac{1-q^{n+1}}{1-q} + q^{n+1} \frac{(1-q)}{1-q} = \frac{1-q^{n+1}}{1-q} + \frac{q^{n+1}-q^{n+2}}{1-q} = \frac{1-q^{n+2}}{1-q}\)
y en el b es aplicarle limite a la formula
Saludos