Question

已知數(shù)列a_n=2n，前n項和為S_n，若數(shù)列{

1

Sn

}的前n項和為T_n，則T₂₀₁₂的值為（　�。�

A． 2012 2011

B． 2010 2011

C． 2013 2012

D． 2012 2013

Answer 1

∵數(shù)列a_n=2n，∴數(shù)列{a_n}是一個等差數(shù)列，∴前n項和S_n=

n(2+2n)

2

=n²+n．
∴

1

Sn

=

1

n(n+1)

=

1

n

-

1

n+1

，
∴T_n=(1-

1

2

)+(

1

2

-

1

3

)+…+(

1

n

-

1

n+1

)=1-

1

n+1

=

n

n+1

．
∴T₂₀₁₂=

2012

2013

．
故選D．