1\( 1*2*3)+ 1\(2*3*4)+ 1\(3*4*5)。 . 1\((n(n+ 1)(n+2))

=[ 1\( 1*2)- 1\(2*3)+ 1\(2*3)- 1\(3*4)+ 1\(3*4)- 1/(4*5)+。 . + 1 \(n(n+ 1)- 1 \(n+ 1)(n+2)]\ 2

=[ 1 \( 1 * 2)- 1 \(n+ 1)(n+2)]/2

= 1 \ 4- 1 \[2(n+ 1)(n+2)]