一道数学简算题1又1/3-7/12+9/20-11/30+13/42-15/56简算求求你们了!我没什么分啦!好的在加啦!

Question

一道数学简算题
1又1/3-7/12+9/20-11/30+13/42-15/56简算
求求你们了!我没什么分啦!好的在加啦!

Answer 1

原式=（1+1/3）-7/(3×4)+9/(4×5)-11/(5×6)+13/(6×7)-15/(7×8)
=1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7+1/8
=1-1/8
=7/8
规律：【n+(n+1)】/【n（n+1）】=（1/n）+1/(n+1)