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(2+1)(2的2次+1)(2的4次+1).(2的2n次+1)等于.
题目详情
(2+1)(2的2次+1)(2的4次+1).(2的2n次+1)等于_____.
▼优质解答
答案和解析
[2+1][2²+1][2⁴+1]…[2 ²ⁿ+1]
=[2-1][2+1][2²+1][2⁴+1]…[2 ²ⁿ+1]
=[2²-1][2²+1][2⁴+1][2八次+1],[2 ²ⁿ+1]
=[2⁴-1][2⁴+1][2八次+1],[2 ²ⁿ+1]
反复用平方差
=2⁴ⁿ-1
=[2-1][2+1][2²+1][2⁴+1]…[2 ²ⁿ+1]
=[2²-1][2²+1][2⁴+1][2八次+1],[2 ²ⁿ+1]
=[2⁴-1][2⁴+1][2八次+1],[2 ²ⁿ+1]
反复用平方差
=2⁴ⁿ-1
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