数列题若log3x=-1/log2 3,则1+x+x^2+…+x^n=
问题描述：
数列题若log3x=-1/log2 3,则1+x+x^2+…+x^n=
答
log3x=-1/log2 3
log3x=-1/log2 3=-log3 2=log3 (1/2)
x=1/2
1+x+x^2+…+x^n=[1-x^(n+1)]/(1-x)
=[1-(1/2)^(n+1)]/(1-1/2)
=2[1-(1/2)^(n+1)]
=2-(1/2)^n