Math — Geometric Series
Partial sums and the sum to infinity of a geometric series.
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a_n = ar^{n-1}
S_n = \frac{a(1 - r^n)}{1 - r}
S_\infty = \frac{a}{1 - r}, \quad |r| < 1
r = \frac{a_{n+1}}{a_n}
Partial sums and the sum to infinity of a geometric series.
a_n = ar^{n-1}
S_n = \frac{a(1 - r^n)}{1 - r}
S_\infty = \frac{a}{1 - r}, \quad |r| < 1
r = \frac{a_{n+1}}{a_n}