1/1*3+1/3*5+1/5*7+...+1/99*101=?(要简便)

1/1*3+1/3*5+1/5*7+...+1/99*101=(1-1/3)÷2+(1/3-1/5)÷2+(1/5-1/7)÷2+……+(1/99-1/101)÷2=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)]÷2=(1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101)÷2中间互相抵消=(1-1/...