How do you find the sum of the infinite geometric series given #3+1.8+1.08+...#?

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Answer 1 · 2016-10-12T13:30:00

The series has a sum of #7.5#.

We use the formula #s_oo = a/(1 - r)# to determine the sum of an infinite convergent geometric series.

In other words, for us to be able to find the sum, #|r| < 1#.

We can find #r# by using the formula #r = t_2/t_1#.

#r = t_2/t_1#

#r = 1.8/3#

#r = 0.6#

We now know #a#, which is #3# and #r#, which is #0.6#.

#s_oo = 3/(1 - 0.6)#

#s_oo = 3/0.4#

#s_oo = 7.5#

Hopefully this helps!