Question

（2013•德州一模）若正項(xiàng)數(shù)列{a_n}滿足1ga_n+1=1+1ga_n，且a₂₀₀₁+a₂₀₀₂+a₂₀₀₃+…a₂₀₁₀=2013，則a₂₀₁₁+a₂₀₁₂+a₂₀₁₃+…a₂₀₂₀的值為（　�。�

A．2013?10¹⁰

B．2013?10¹¹

C．2014?10¹⁰

D．2014?10¹¹

Answer 1

分析：由對(duì)數(shù)式可得正項(xiàng)數(shù)列{a_n}為等比數(shù)列，且公比q=10，而所求的式子等于（a₂₀₀₁+a₂₀₀₂+a₂₀₀₃+…a₂₀₁₀）q¹⁰，代值可得．

解答：解：由題意可得1ga_n+1-1ga_n=lg

an+1

an

=1，即

an+1

an

=10，
所以正項(xiàng)數(shù)列{a_n}為等比數(shù)列，且公比q=10，
所以a₂₀₁₁+a₂₀₁₂+a₂₀₁₃+…a₂₀₂₀
=（a₂₀₀₁+a₂₀₀₂+a₂₀₀₃+…a₂₀₁₀）q¹⁰=2013•10¹⁰，
故選A

點(diǎn)評(píng)：本題考查等比數(shù)列的判斷和等比數(shù)列的性質(zhì)，屬中檔題．