Answer:
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.
