Question

等差数列{a n }中，a 7 =4，a 19 =2a 9 ，

Answer 1

（I）设等差数列{a _n}的公差为d

∵a ₇=4，a ₁₉=2a ₉，

∴

a 1 +6d=4

a 1 +18d=2( a 1 +8d)

解得，a ₁=1，d=

1

2

∴ a n =1+

1

2 (n-1) =

1+n

2

（II）∵ b n =

1

n a n =

2

n(n+1) =

2

n -

2

n+1

∴s _n= 2(1-

1

2 +

1

2 -

1

3 +…+

1

n -

1

n+1 )

= 2(1-

1

n+1 ) =

2n

n+1