1/1*2*3+1/2*3*4+1/3*4*5+.+1/n(n+1)(n+2)+.sn=1/2*[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)]=1/2*[1/2-1/(n+1)(n+2)]=1/4-1/2(n+1)(n+2)limsn=1/4所以级数的和为1/4.如果用幂级数求和怎么做呢 就是我追加的问题的那个做法那太麻烦了!不必要!要加分哦!嘿嘿!应该:s(x)=Σ1/n(n+1)(n+2)*x^(n+2)两边求导得s'(x)=Σ1/n(n+1)*x^(n+1)再求导得s''(x)=Σ1/n*x^n再求导得s'''(x)=Σx^(n-1)=1/(1-x)n从1到无穷大!连续积分!再代特殊值!如s(0)=0=s'(0)=s''(0)等,最后求出s(x)!令x=1,即可!