初二数学题,求解!
2个回答
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原式= (1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/10)(1-1/10)
= (1+1/2)(1+1/3)...(1+1/10)(1-1/2)(1-1/3)...(1-1/10)
= 3/2 * 4/3 ... 11/10 * 1/2 * 2/3 ... 9/10
= (3 * 4 ... 11)/(2 * 3 ... 10) * (1 * 2 ... 9)/ (2 * 3 ... 10)
= 11/2 * 1/10
= 11 / 20
= (1+1/2)(1+1/3)...(1+1/10)(1-1/2)(1-1/3)...(1-1/10)
= 3/2 * 4/3 ... 11/10 * 1/2 * 2/3 ... 9/10
= (3 * 4 ... 11)/(2 * 3 ... 10) * (1 * 2 ... 9)/ (2 * 3 ... 10)
= 11/2 * 1/10
= 11 / 20
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