已知数列{an}中,an=1/n(n+2).求n趋向正无穷大时Sn的极限?_数学解答

已知数列{an}中,an=1/n(n+2).求n趋向正无穷大时Sn的极限?

人气：133 ℃　时间：2020-06-15 02:48:55

解答

an=1/n(n+2)=1/2*(1/n-1/(n+2))Sn=a1+a2+.+an=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/(n-2)-1/n+1/(n-1)-1/(n+1)+1/n-1/(n+2))=1/2(1+1/2-1/(n+1)-1/(n+2))=1/2(3/2-(2n+3)/(n^2+3n+2)=(3n^2+5n)/2(n^2+3n+2)=(3+5...