求数列1/1+2,1/1+2+3,···,1/1+2+···+(n+1)前n项和,要过程

问题描述:

求数列1/1+2,1/1+2+3,···,1/1+2+···+(n+1)前n项和,要过程

1/1+2+···+(n+1)=1/{[1+(n+1)](n+1)/2}=2/(n+1)(n+2)所以,S=2[1/2x3+1/3x4+……+1/(n+1)(n+2)]=2[(1/2-1/3)+(1/3-1/4)……+(1/(n+1))-1/((n+2))]=2[1/2-1/(n+2)]=n/(n+2)