等差数列中前三项的分别为x,2x,5x-4,前n项和为Sn且Sk=42求Tn=1/S1+1/S2+1/S3+...+1/Sn
问题描述:
等差数列中前三项的分别为x,2x,5x-4,前n项和为Sn且Sk=42求Tn=1/S1+1/S2+1/S3+...+1/Sn
答
等差数列中前三项的分别为x,2x,5x-4,∴4x=x+5x-4,得X=2,2X=4,5x-4=6Sn=n(n+1)Tn=1/S1+1/S2+1/S3+...+1/Sn=1/1*2+1/2*3+---+1/n(n+1)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+---+(1/n-1/(n+1))=1-1/(n+1)=n/(n+1...