Question

1*2分之1+2*3分之一+3*4分之一一直加到n*(n+1)分之一

Answer 1

1*2分之1+2*3分之一+3*4分之一+……+n*(n+1)分之一
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

Answer 2

=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+1)
=(n²+n+n+1-n)/n(n+1)
=(n²+n+1)/(n²+n)