The Limiting Sum of a Geometric Series (HSC SSCE Mathematics Advanced): Flashcards

$|r| < 1$ or $-1 < r < 1$

$S_{infty} = \frac{a}{1-r}$

$r^n \to 0$

$\lim_{n \to \infty} T_n = 0$

No limiting sum; series does not converge

The series has a limiting sum

$S_{\infty}$ or $S$

$T_n = ar^{n-1}$

$S_n = \frac{a(1-r^n)}{1-r}$

$\sum_{n=1}^{\infty} ar^{n-1} = \frac{a}{1-r}$