在以d为公差的等差数列an中,设S1=a1+a2.+an,S2=an+1+an+2+a2n,S3=a2n+1+a2n+a3n,求证_数学解答

在以d为公差的等差数列an中,设S1=a1+a2.+an,S2=an+1+an+2+a2n,S3=a2n+1+a2n+a3n,
求证S1,S2,S3,也是等差数列,并求其公差

人气：443 ℃　时间：2019-10-24 11:38:21

解答

S2-S1=(an+1-a1)+(an+2-a2)+...+(a2n-an)=nd*n=d*n^2
S3-S2=(a2n+1-a1)+(a2n+2-a2)+...+(a3n-a2n)=nd*n=d*n^2
等差数列,且公差为d*n^2