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(1-1/4)*(1-1/9)*(1-1/16)*.*(1-1/361)*(1-1/400)=?
题目详情
(1-1/4)*(1-1/9)*(1-1/16)*.*(1-1/361)*(1-1/400)=?
▼优质解答
答案和解析
(1-1/4)(1-1/9)(1-1/16).(1-1/10000)
=(1-1/2^2)(1-1/3^2).(1-1/20^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/20)(1+1/20)
=1/2*3/2*2/3*4/3.19/20*21/20
=21/2
=(1-1/2^2)(1-1/3^2).(1-1/20^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/20)(1+1/20)
=1/2*3/2*2/3*4/3.19/20*21/20
=21/2
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