Geometric Series (Edexcel A-Level Mathematics): Flashcards

The sum approaches infinity as more terms are added.

It converges if $|r| < 1$, with $S_n$ approaching $S_\infty$.

$S_\infty = \frac{a}{1 - r}$, for $|r| < 1$.

The sum increases without bound as $n$ approaches infinity.

$S_\infty = 6 / (1 - 1/3) = 9$.

$S_\infty$ equals the first term divided by $(1 - r)$, where $r < 1$.

$S_n = a(1 - r^n) / (1 - r)$.

Set $a / (1 - r) = 4a$, leading to $r = 3/4$.

Set $a*r^2 = 9$ and solve for $a$ with $r$ known.

$S_n = a(1 - r^n) / (1 - r)$ for $|r| < 1$