(1-2^2/1)(1-3^2/1)(1-4^2/1)…(1-99^2/1)(1-100^2/10) 简便方法计算

问题描述:

(1-2^2/1)(1-3^2/1)(1-4^2/1)…(1-99^2/1)(1-100^2/10) 简便方法计算
1个回答 分类:数学 2014-10-20

问题解答:

我来补答
题目应是(1-2^2/1)(1-3^2/1)(1-4^2/1)…(1-99^2/1)(1-100^2/1)
=(1-2/1)(1+2/1)(1-3/1)(1+3/1).(1-99/1)(1+99/1)(1-100/1)(1+100/1)
=(1-2/1)(1-3/1).(1-99/1)(1-100/1)(1+2/1)(1+3/1).(1+99/1)(1+100/1)
=(2/1)(3/2).(99/98)(100/99) (2/3)(3/4).(99/100)(100/101)
=(100/1) (2/101)
=200/101
 
 
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