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Question
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`2, 4/3, 8/9, 16/27, ...`
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Solution
`2, 4/3, 8/9, 16/27, ...`
`"a" = 2, "r" = (4/3)/2 = 2/3, |"r"| < 1`
∴ Sum to infinity exists.
Sum to infinity = `"a"/(1 - "r")`
= `2/(1 - 2/3)`
= 6
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