Infinte Geometric Series

Algebra Level 2

Find the formula for the sum $S$ of any infinite geometric series, where $r$ is the common ratio less than 1 but more than -1 and $a$ is the first term.

S = {a}\cdot{(1-r)}

S = \frac{a}{1-r}

S = \frac{1-r}{a}

S = \frac{a}{r-1}

1 solution

X X
Jul 22, 2018

$1 S=a(1+r+r^2+r^3+...)$ ...(1)

$rS=a(r+r^2+r^3+r^4...)$ ...(2)

$(1-r)S=a$ ...(1)-(2)

$S=\dfrac a{1-r}$

Infinte Geometric Series

1 solution

0 pending reports