Question

等比数列{an}中,公比q=2,log2a1+log2a2+log2a3+...+log2a10=25,则a1+a2+.

Answer 1

log2a1+log2a2+log2a3+...+log2a10=25

log2(a1*a2*……*a10)=25

log2(a1*a1q*a1q²*……*a1*q^9)=25

log2(a1^10*q^(1+2+……+9))=25

a1^10*q^45=2^25

q=2

所以a1^10=2^25÷2^45=2^(-20)

真数大于0

a1>0

所以a1=2^(-2)=1/4

所以a1+a2+……+a10

=1/4*(1-2^10)/(1-2)

=1023/4