Maths — Geometric Series
nth term, partial sum and sum to infinity.
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a_n = a r^{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}
nth term, partial sum and sum to infinity.
a_n = a r^{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}