1+19/6+61/12+141/20+271/30+463/42+729/56+1081/72+1531/90=

题目

1+19/6+61/12+141/20+271/30+463/42+729/56+1081/72+1531/90=
”/”是分数线
请写解题思路

答案

1+19/6+61/12+141/20+271/30+463/42+729/56+1081/72+1531/90
=1+(3+1/6)+(5+1/12)+(7+1/20)+(9+1/30)+(11+1/42)+(13+1/56)+(15+1/72)+(17+1/90)
=(1+3+5+7+9+11+13+15+17) +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+17)*9/2 +(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)
=81+1/2-1/10
=81又2/5