Question

2/1*3+2/2*4+2/3*5+.....+2/n(n+2)=？求解

Answer 1

2/1*3+2/2*4+2/3*5+.....+2/n(n+2)

=1-1/3+1/2-1/4-1/3-1/5+……+1/n-1/(n+2)

=1+1/2-1/(n+1)-1/(n+2)

=3/2-(2n+3)/[n+1)(n+2)]

Answer 2

3n^2+5n/2n^2+6n+4
原式=2*（1/李桐1*3+2/2*4……）
=2*1/2*（1-1/3+1/2-1/4……1/（n-1）-1/（n+1）+1/n-1/（哪野坦n-2））
=1+1/2-1/脊猜（n-1）-1/(n-2)
=3n^2+5n/2n^2+6n+4