化简1*2分子1+2*3分之1+3*4分之1+n(n+1)分之1=

2025-04-24 08:59:20
推荐回答(2个)
回答1:

1*2分子1+2*3分之1+3*4分之1+n(n+1)分之1
=1-1/2+1/2-1/3+1/3-1/4……+1/n-1/(n+1)
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1)
望采纳

回答2:

1*2分之1+2*3分之1+3*4分之1+n(n+1)分之1
=1-1/2+1/2-1/3+1/3-1/4+1/4……+1/n-1/(n+1)
=1-1/(n+1)
=(n+1-1)/(n+1)
=n/(n+1)