等比an,an=1/3n次.设bn=log3a1+log3a2+...+log3an 求1/bn前n项和

问题描述:

等比an,an=1/3n次.设bn=log3a1+log3a2+...+log3an 求1/bn前n项和

bn=log3a1+log3a2+...+log3an=log(3)(a1a2a3a4a5a6..an)=log(3)(1/3×1/3^2+1/3^3×...×1/3^n)=log(3)[3^(-1-2-3-..-n)=-n(n+1)/2∴1/bn=-2/n(n+1)=-2[1/n-1/(n+1)]∴Sn=-2×[1-1/2+1/2-1/3+..+1/n-1/(n+1)]=-2×(1...