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Question
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Solution
Here, t1 = 0.5, t2 = 0.05, t3 = 0.005
∴ `"t"_2/"t"_1 = 0.05/0.5` = 0.1 and `"t"_3/"t"_2 = 0.005/0.05` = 0.1
∴ The given sequence is a G.P.
∴ a = 0.5 and r = 0.1
∴ Sn = `("a"(1 - "r"^"n"))/(1 - "r")`, for r < 1
= `(0.5[1 - (0.1)^"n"])/(1 - 0.1)`
= `0.5/0.9 [1 - (0.1)^"n"]`
= `5/9[1 - (1/10)^"n"]`
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