Progresión geométrica:
\[ \sum_{k=N_1}^{N_2} a r^k = a \frac{r^{N_1}-r^{N_2+1}}{1-r} \]
\[ \sum_{k=0}^{\infty} a r^k = \frac{a}{1-r}\text{ para |r|<1} \]
Progresión aritmética de \(n\) términos:
\[ \sum_{k=1}^{M} k = \frac{n \left(k_1 + k_M\right)}{2}\]
By Vincent Pantaloni – Own work, CC BY-SA 4.0, Link