Find the sum of the given geometric series: 60 + 6 + 0.6 + 0.06 + 0.006

Answer 1

There is no ..., so my assumption is that there are only 5 terms.

Given the terms present, it is so easy to just write the answer - 66.666

If one were solving this in general, the ratio is 1/10, and there are 5 terms, so the sum is

a(1 - r^n)/(1-r) = 60(1 - .1^5)/(1 - .1) = 60(.99999)/.9 = 60 * 1.1111 = 66.666

Answer 2

sum = 66.666... = 66 2/3

You can probably see that, without the formula, but

as a geometric series, the common ratio = 1/10 or 0.1 = r, first term = a = 60

the formula for Sum of an infinite series = S = a/(1-r) = 60/(1-.1) = 60/(.9) = 60(10/9) =600/9 = 66.666.... = 66 2/3 or 200/3

Answer 3

If this infinite sum then S = a₁/(1 - r) = 60/(1 - 0.1) = 60/0.9 = 200/3