To find the sum of an infinite series, use this following formula
S∞ = [tex] \dfrac{a_{1}}{1-r} [/tex]
with S∞ as the sum of infinite series, a₁ as the first term of the series, and r as the ratio.
First, find the ratio of the series
The ratio can be defined using division of the nth term by the (n-1)th term. Or if you use a₂, the divisor will be a₍₂₋₁₎ = a₁
r = a₂/a₁
r = [tex] \dfrac{12}{72} [/tex]
r = [tex] \dfrac{1}{6} [/tex]
The ratio of the series is 1/6
Second, calculate the sum using the formula above.
S∞ = [tex] \dfrac{a}{1-r} [/tex]
Plug in the numbers
S∞ = [tex] \dfrac{72}{1- \frac{1}{6} } [/tex]
Write the division horizontally
S∞ = 72 ÷ [tex](1-\frac{1}{6})[/tex]
1 can be written as 6/6
S∞ = 72 ÷ [tex] (\frac{6}{6} -\frac{1}{6} )[/tex]
S∞ = 72 ÷ [tex] \frac{5}{6} [/tex]
Change the division into multiplication
S∞ = 72 × [tex] \frac{6}{5} [/tex]
S∞ = [tex] \frac{432}{5} [/tex]
S∞ = 86.4
The sum of the series is 86.4
