1/56+1/72+1/90+1/110 2/3+2/9+2/27+2/81+2/243+2/729

题目

1/56+1/72+1/90+1/110 2/3+2/9+2/27+2/81+2/243+2/729
两道题是分开的。打错了。应该是2/3+2/9+2/27+2/81+2/243+2/729

答案

1题：
1/56+1/72+1/90+1/110
=(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)
=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11
=1/7-1/11
=11/77-7/77
=4/77
2题：
2/3+2/9+2/27+2/81+2/243+2/729
=(1-1/3)+(1/3-1/9)+(1/9-1/27)+(1/27-1/81)+(1/81-1/243)+(1/243-1/729)
=1-1/3+1/3-1/9+1/9-1/27+1/27-1/81+1/81-1/243+1/243-1/729
=1-1/729
=728/729