1、1/1*2+1/2*3+1/3*4+1/4*5+……+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
=1-1/100
=99/100
2、1/1*2+1/2*3+1/3*4+1/4*5+……+1/n*(n+1)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1、1/1*2+1/2*3+1/3*4+1/4*5+……+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
=1-1/100
=99/100
2、1/1*2+1/2*3+1/3*4+1/4*5+……+1/n*(n+1)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)