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.

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yes, gavin is right.

step-by-step explanation:

gavin is correct. 

this problem is about converting 9% per year to how many percent per quarter. the rate is still the same. it only differed in the time period. so, through dimensional analysis,

9% per year  × (1 year / 4 quarters) = 2.25% per quarter

if he was asked to convert 9% per year to how many percent per quarter  compounded quarterly, then you will not simply divide by four. this is because compounding is not linear.

hope this , have a good day. c;