计算 1/2+1/6+1/12+1/20+1/30.+1/1101/2+1/6+1/12+1/20+1/30.+1/110 写出计算过程

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计算 1/2+1/6+1/12+1/20+1/30.+1/1101/2+1/6+1/12+1/20+1/30.+1/110 写出计算过程
计算 1/2+1/6+1/12+1/20+1/30.+1/110
1/2+1/6+1/12+1/20+1/30.+1/110 写出计算过程

计算 1/2+1/6+1/12+1/20+1/30.+1/1101/2+1/6+1/12+1/20+1/30.+1/110 写出计算过程
1/2 = 1/1*2 = 1/1-1/2
1/6 =1/2*3 = 1/2-1/3
1/12 = 1/3*4 = 1/3-1/4
.
1/90 = 1/9*10 = 1/9 - 1/10
1/110 = 1/10*11 = 1/10 -1/11
所以原式=1/1-1/2+1/2-1/3+1/3.-1/9+1/9-1/10+1/10-1/11=1-1/11=10/11

1/2+1/6+1/12+1/20+1/30+....+1/110
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/10-1/11
=1-1/11
=10/11

原式=1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+……+1(10x11)
=1/1-1/2+1/2-1/3+1/3-1/4+.....+1/10-1/11
=1-1/11
=10/11