Question

设{a_n}是正数等差数列，{b_n}是正数等比数列，且a₁=b₁，a_2n+1=b_2n+1，则______．

Answer 1

因为等差数列{a_n}和等比数列{b_n}各项都是正数，且a₁=b₁，a_2n+1=b_2n+1，
所以a_n+1-b_n+1=

a1+a2n+1

2

-

b1•b2n+1

=

a1+a2n+1-2 a1•a2n+1

2

=

( a1 - a2n+1 ) 2

2

≥0．
即 a_n+1≥b_n+1．
故答案为：a_n+1≥b_n+1．