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设{a_n}为等差数列,{b_n}为等比数列,则数列C_n=a_n·b_n一定可化为C_n=(An+B)·q~n的形式,这类数列的求和通常都采用错位相减法。例1设数列{a_n}的通项公式为a_n=(2n-1)·(1/2)~n,求其前n项和S_n。解法1(错位相减法):设S_n=1×1/2+3×1/2~2+5×1/2~3+…+(2n-1)·1/2~n,
Let {a_n} be an arithmetic progression and {b_n} be a geometric progression. The sequence C_n = a_n · b_n must be formally C_n = (An + B) · q ~ n. The sum of these series is usually Displacement subtraction method. Example 1 Suppose the general formula of the sequence {a_n} is a_n = (2n-1) · (1/2) ~n, find the first n terms and S_n. Solution 1 (Displacement Subtraction Method) Let S_n = 1 × 1/2 + 3 × 1/2 ~ 2 + 5 × 1/2 ~ 3 + ... + (2n-1) · 1/2 ~