This is the concrete application of the idea of decomposition and combination in the summation of series. The essence of the split term method is to decompose each term (general term) in the series and then recombine it to eliminate some terms. Finally, the purpose of summation is achieved. The general term decomposition (split term) is as follows: (1)1/n (n+1) =1/n-1(n+1) (2) 6544.

Example: in a series an =1[n (n+2)], find the first n terms and Sn.

∫ an =1/[n (n+2)] = [(1/n)-1/(n+2)]/2 (split term elimination)

∴sn=[ 1-( 1/3)+( 1/2)-( 1/4)+( 1/3)-( 1/5)+…+( 1/n)- 1/(n+2)]/2

=(3/2)-(2n+3)/(n+ 1)(n+2)。