解答简便运算1/6+1/12+1/20+1/30+1/42+1/561/5*6+1/6*7+1/7*8+……+1/48*49+1/49*501/3+1/15+1/35+1/63+1/99

Answer 1

1/6+1/12+1/20+1/30+1/42+1/56=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1/2-1/8=3/8
1/2-1/3=1/6 1/3-1/4=1/12依此类推1/7-1/8＝1/56再去掉括号,加减的都能消去,只剩下第一个1/2和最后一个,1/8再相减就得3/8