Question

高一数学 数列求和

该数列的前2n项和为
感谢各位的帮助，但是是前2n项和，思路可采纳

Answer 1

奇数项公比＝2,a1=1
偶数项公比＝1/2,a2=1/2
Sn=[a1+a3+……+a(2n-1)]+[a2+a4+……+a2n]
=a1*(1-2^n)/(1-2)+a2*[1-(1/2)^n]/(1-1/2)
=2^n-1+1-1/2^n
=2^n-1/2^n

Answer 2

奇偶分开算，（2^0+2^1+...+2^（n-1）/2）+(2^-1+2^-2+...2^(-n/2))=(2^n - 1)+(1-1/2^n)=2^n-1/2^n

Answer 3

假设在单元格A1中输入n值，在B1单元格输入公式即可
=SUMPRODUCT(2^(ROW(INDIRECT("A1:A"&A1*2))/2-1/2),MOD(ROW(INDIRECT("A1:A"&A1*2)),2))+SUMPRODUCT(2^(-ROW(INDIRECT("A1:A"&A1*2))/2),MOD(ROW(INDIRECT("A1:A"&A1*2))+1,2))

Answer 4

可以用一楼的思路