give an example of a convergent infinite series whose sum equal 3/5. explain how you know your series converges and write out work to show that its sum is in fact 3/5

The series 1/5, 2/15, 4/45, 8/135 ... converges and sums up to 3/5

Step-by-step explanation:

Consider the infinite geometric series

1/5, 2/15, 4/45, 8/135 ...

With first term, a=1/5

common ratio, r = ⅔

The series converge because the common ratio, |r|<1.

The sum to infinity of a geometric series, S = a / (1-r)

S = 1/5 : (1-⅔) = 1/5 : 1/3 = 3/5

Therefore, the geometric series 1/5, 2/15, 4/45, 8/135 ... sums up to 3/5.