1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90简便计算

Answer 1

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1-1/10=9/10