数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 05:20:23
数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]

数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]
数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]
数列求和:
lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]

数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]数列求和:lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2n-1)]
偶感觉题目有点问题
题目如果是lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2^(n-1))]的话,偶做法如下:
lg1/3+lg10/(3^2)+lg100/(3^4)+lg1000/(3^8)……+lg[10^(n-1)]/[3^(2^(n-1))]=lg[1*10*100*……*10^(n-1)]/[3*3^2*3^4*……*3(2^(n-1))]
=lg10^[0+1+2+3+……+(n-1)]-lg3^[1+2+4+……+2^(n-1)]
=n(n+1)/2-(2^n-1)lg3