求大神解第三题
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有题目可知
a²-b²=(a+b)(a-b)
(1-(1/2)²)(1-(1/3)²)(1-(1/4)²)(1-(1/5)²)……(1-(1/99)²)(1-(1/100)²)
=(1-(1/2))(1+(1/2))(1-(1/3))(1+(1/3))(1-(1/4))(1+(1/4))(1-(1/5))(1+(1/5))……(1-(1/99))(1+(1/99))(1-(1/100))(1+(1/100))
=(1/2)*(101/100)
=101/200
a²-b²=(a+b)(a-b)
(1-(1/2)²)(1-(1/3)²)(1-(1/4)²)(1-(1/5)²)……(1-(1/99)²)(1-(1/100)²)
=(1-(1/2))(1+(1/2))(1-(1/3))(1+(1/3))(1-(1/4))(1+(1/4))(1-(1/5))(1+(1/5))……(1-(1/99))(1+(1/99))(1-(1/100))(1+(1/100))
=(1/2)*(101/100)
=101/200
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