求和Sn=1*(1/3)+3*(1/3)^2+5*(1/3)^3+.+(2n-1)*(1/3)^n求和Sn=1*(1/3) + 3_数学解答

求和Sn=1*(1/3)+3*(1/3)^2+5*(1/3)^3+.+(2n-1)*(1/3)^n
求和Sn=1*(1/3) + 3*(1/3)^2 + 5*(1/3)^3 +.+(2n-1)*(1/3)^n

人气：487 ℃　时间：2020-06-02 19:07:29

解答

等差乘等比求和的思想是乘积求差法:数列乘公比再与原数列求差Sn=1*(1/3)+3*(1/3)^2+5*(1/3)^3+.+(2n-1)*(1/3)^n那么(1/3)*Sn=1*(1/3)^2+3*(1/3)^3+5*(1/3)^3+.+(2n-1)*(1/3)^(n+1)上减下得(2/3)*Sn=2*(1/3)^2+2*(1/3...