求和1x2+3x2^2+5x2^3+…+(2n-1)x2n要详解答案,我采纳!急用!

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求和1x2+3x2^2+5x2^3+…+(2n-1)x2n要详解答案,我采纳!急用!

求和1x2+3x2^2+5x2^3+…+(2n-1)x2n要详解答案,我采纳!急用!
求和1x2+3x2^2+5x2^3+…+(2n-1)x2n要详解答案,我采纳!急用!

求和1x2+3x2^2+5x2^3+…+(2n-1)x2n要详解答案,我采纳!急用!
Sn=1×2+3×2^2+5×2^3+...+(2n-1)×2^n
2Sn=1×2^2+3×2^3+...+(2n-3)×2^n+(2n-1)×2^n
Sn-2Sn=-Sn=-2+2×2+2×2^2+...+2×2^n-(2n-1)×2^n=-2+2(2^n-1)/(2-1)-(2n-1)×2^n
Sn=(2n-3)×2^n+4