Question

Sn=2

1

3

+4

1

9

+6

1

27

+…+(2n+

1

3n

)=______．

Answer 1

Sn=2

1

3

+4

1

9

+6

1

27

+…(2n+

1

3n

)
=(2+4+6+…+2n)+(

1

3

+

1

9

+…+

1

3n

)
=

2+2n

2

×n+

1 3 (1- 1 3n )

1- 1 3

=n(n+1)+

1-( 1 3 )n

2

故答案为：n(n+′1)+

1-( 1 3 )n

2