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1/8+1/24+1/48+1/80+.+1/360的答案是多少

题目详情
1/8+1/24+1/48+1/80+.+1/360的答案是多少
▼优质解答
答案和解析
1/8+1/24+1/48+1/80+.+1/360
1/(2x4)+1/(4x6)+1/(6x8)+…+1/(18x20)
=(1/2)x[2/(2x4)+2/(4x6)+2/(6x8)+…+2/(18x20)]
=(1/2)x(1/2-1/4+1/4-1/6+1/6-1/8+…+1/18-1/20)
=(1/2)x(1/2-1/20)
=9/40
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