Find the sum of the infinite geometric series sigmainfinityi

Find the sum of the infinite geometric series. sigma^infinity_i = 1 44(0.6)^i - 1 sigma^infinity_i = 1 44(0.6)^i - 1 = (Round to two decimal places.)

Solution

This is a geometric series with first term 44 and common ratio 0.6 (see geometric series ).
The common ratio is less than 1 in absolute value, so that the series is convergent and its sum is given by

S= (first term)/(1common ratio)

S = a/(1-r) for infinite series.

= 44 /(1-0.6)

= 44/0.4

= 110