Question

（2012•淄博一模）已知數(shù)列{a_n}滿足a₁=1，且

an+1

an

=

n+1

n

，則a₂₀₁₂=（　�。�

A．2010

B．2011

C．2012

D．2013

Answer 1

分析：

an+1

an

=

n+1

n

，考慮利用疊乘

a2

a1

•

a3

a2

…

an

an-1

=

2

1

×

3

2

…×

n

n-1

=

an

a1

求得a_n，進(jìn)而可求答案．

解答：解：∵

an+1

an

=

n+1

n

，a₁=1
∴

a2

a1

•

a3

a2

…

an

an-1

=

2

1

×

3

2

…×

n

n-1

=

an

a1

=n
∴a_n=na₁=n，a₂₀₁₂=2012
故選C

點(diǎn)評：本題主要考查了數(shù)列的遞推式．解題的關(guān)鍵是從遞推式中找到規(guī)律，進(jìn)而利用疊乘求得數(shù)列的通項(xiàng)公式．