1/(1*2*3)+1/(2*3*4)+1/(3*4*5)…………=?极限求和
问题描述：
1/(1*2*3)+1/(2*3*4)+1/(3*4*5)…………=?极限求和
答
1/[n(n+1)(n+2)]=(1/2)[1/n(n+1)-1/(n+1)(n+2)]1/(1*2*3)+1/(2*3*4)+1/(3*4*5)…………=(1/2)(1/1*2-1/2*3)+(1/2)(1/2*3-1/3*4)+...+(1/2)[1/n(n+1)-1/(n+1)(n+2)]=(1/2)[1/1*2-1/(n+1)(n+2)]=[n(n+3)]/[4(n+1)(n+...