题目

2的平方减1分之1加3的平方减1分之1.加20的平方减1分之1等于多少

提问时间：2020-07-27

答案

1/(2²-1)+1/(3²-1)+1/(4²-1)+.+1/(20²-1)
=1/(1×3)+1/(2×4)+1/(4×4)+.+1/(19×21)
=1/2(1-1/3)+1/2(1/2-1/4)+1/2(1/3-1/5)+.+1/2(1/18-1/19)+1/2(1/19-1/21)
=1/2[(1-1/3)+(1/2-1/4)+(1/3-1/5)+.+(1/18-1/20)+(1/19-1/21)]
=1/2[1+1/2-1/20-1/21]
=1/2(3/2-41/420)
=589/840