若数列{an}是公比为q的等比数列,且bn=lgan,求证{bn}为等差数列
问题描述:
若数列{an}是公比为q的等比数列,且bn=lgan,求证{bn}为等差数列
答
设an=a1*q^(n-1),那么bn=lgan=lg(a1*q^(n-1))=lga1+(n-1)lgq,所以b(n+1)-bn=lgq是常数,所以{bn}是等差数列
若数列{an}是公比为q的等比数列,且bn=lgan,求证{bn}为等差数列
设an=a1*q^(n-1),那么bn=lgan=lg(a1*q^(n-1))=lga1+(n-1)lgq,所以b(n+1)-bn=lgq是常数,所以{bn}是等差数列