Answer: 15/4 = 3.75
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Work Shown
This appears to be a geometric sequence with the following properties:
- a = 3 = first term
- r = 1/5 = common ratio
Because -1 < r < 1 is true, it means the sum of infinitely many terms can be computed with the formula below.
S = a/(1 - r)
S = 3/(1 - 1/5)
S = 3/(4/5)
S = 3*(5/4)
S = 15/4
The final answer is 15/4
It means that 3 + (3/5) + (3/25) + .... = 15/4
15/4 = 3.75 exactly.
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Let's look at a few partial sums
- 3 + (3/5) = 3.6
- 3 + (3/5) + (3/25) = 3.72
- 3 + (3/5) + (3/25) + (3/125) = 3.744
- 3 + (3/5) + (3/25) + (3/125) + (3/625) = 3.7488
- 3 + (3/5) + (3/25) + (3/125) + (3/625) + (3/3125) = 3.74976
- 3 + (3/5) + (3/25) + (3/125) + (3/625) + (3/3125) + (3/15625) = 3.749952
- 3 + (3/5) + (3/25) + (3/125) + (3/625) + (3/3125) + (3/15625) + (3/78125) = 3.7499904
As you can see, the partial sums are slowly approaching 15/4 = 3.75, which would help us somewhat confirm the answer. Unfortunately we cannot fully confirm the answer because we'd need infinitely many terms to do so.