2+ 2^3 +2^5 +...+(2^2n-3) +(2^2n-1)=?_数学解答

2+ 2^3 +2^5 +...+(2^2n-3) +(2^2n-1)=?

人气：479 ℃　时间：2020-06-13 13:55:11

解答

2+ 2^3 +2^5 +...+(2^2n-3) +(2^2n-1)=x
4[2+ 2^3 +2^5 +...+(2^2n-3) +(2^2n-1)]=4x=2^3 +2^5 +...+(2^2n-3) +(2^2n-1)+(2^2n+1)
3x=(2^2n+1)-2
x=2[(2^2n)-1]/3
2+ 2^3 +2^5 +...+(2^2n-3) +(2^2n-1)=2[(2^2n)-1]/3