等比数列an的前n项和为2^n—1，则数列an^2的前n项和为多少？
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∵ 前n项和为 2^n-1
∴ S1 = 2-1 = 1
S2 = 2² - 1 = 3
S3 = 2³ - 1 = 7
S4 = 2⁴ - 1 = 15
........
∴ a1 = S1 = 1
a2 = S2 - S1 = 3-1 = 2
a3 = S3 - S2 = 7-3 = 4
a4 = S4 - S3 = 15-7 = 8
.......
则 数列an的公比 q=2
那么， 数列(an)²的公比 q' = q² = 4
数列(an)²的前n项和为
(4^n - 1) / (4 - 1) = (4^n-1) /3
∴ S1 = 2-1 = 1
S2 = 2² - 1 = 3
S3 = 2³ - 1 = 7
S4 = 2⁴ - 1 = 15
........
∴ a1 = S1 = 1
a2 = S2 - S1 = 3-1 = 2
a3 = S3 - S2 = 7-3 = 4
a4 = S4 - S3 = 15-7 = 8
.......
则 数列an的公比 q=2
那么， 数列(an)²的公比 q' = q² = 4
数列(an)²的前n项和为
(4^n - 1) / (4 - 1) = (4^n-1) /3
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