n(n+1)/1+(n+1)(n+2)/1+.+(n+2007)(n+2008)/1=?

问题描述:

n(n+1)/1+(n+1)(n+2)/1+.+(n+2007)(n+2008)/1=?

用裂项法:
1/(n+1)(n+2)=1/(n+1)-1/(n+2)
各项同相处理,再相加,抵消得:
所以其和=1/(n+1)-1/(n+2008)