级数n/(n+1)(n+2)(n+3)和是多少_数学解答

级数n/(n+1)(n+2)(n+3)和是多少

人气：311 ℃　时间：2020-09-15 19:34:37

解答

n/(n+1)(n+2)(n+3)=(n+1-1)/(n+1)(n+2)(n+3)=1/(n+2)(n+3)-1/(n+1)(n+2)(n+3)=[1/(n+2)-1/(n+3)]-(1/2)[1/(n+1)(n+2)-1/(n+2)(n+3)],求和得到1/3-(1/2)*(1/(2*3))=1/4.