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Question
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
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Solution
Here, a = p, r = `"q"/"p"`
If `"q"/"p"` < 1, then
∴ Sn = `("a"(1 - "r"^"n"))/(1 - "r")`
= `("p"[1 - ("q"/"p")^"n"])/(1 - ("q"/"p")`
= `"p"^2/("p" - "q") [1 - ("q"/"p")^"n"]`
If `"q"/"p" > 1,` then
Sn = `("a"("r"^"n" - 1))/("r" - 1)`
= `("p"[("q"/"p")^"n" - 1])/(("q"/"p") - 1)`
= `"p"^2/("q" - "p") [("q"/"p")^"n" - 1]`
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