简单计算题
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
[ 1/6=1/( )-1/( ) 1/12=1/( )-1/( ) 1/20=1/( )-1/( )...... ]
(上面属于一道题，请算出最后等于多少？）
参考答案:解：
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+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10
这种方法在数学中叫做裂项相消法。