解
1/2+(-1/6)+(-1/12)+……+(-1/42)
=1/2-(1/6+1/12+……+1/42)
=1/2-[(1/2-1/3)+(1/3-1/4)+……+(1/6-1/7)]
=1/2-[1/2+(1/3-1/3)+(1/4-1/4)+……+(1/6-1/6)-1/7]
=1/2-1/2+1/7
=1/7
1/6=1/2-1/3
1/12=1/3-1/4
…………