When n= 1,/s1=1a1=1(1+1) =/kloc-.

a 1=2

When n≥2,

1/S 1+ 1/S2+...+ 1/Sn = n/(n+ 1)( 1)

1/s1+1/S2+...+1/sec (n- 1)=(n- 1)/n (2)

( 1)-(2)

1/Sn = n/(n+ 1)-(n- 1)/n =[n？ -(n+ 1)(n- 1)]/[n(n+ 1)]=(n？ -n？ + 1)/[n(n+ 1)]= 1/(n？ +n)

Sn=n？ +n

S(n- 1)=(n- 1)？ +(n- 1)

an=Sn-S(n- 1)=n？ +n-(n- 1)？ -(n- 1)=2n

When n= 1, a 1=2, which also satisfies the general formula.

The general formula of sequence {an} is an=2n.

bn=( 1/2)^(an)=( 1/2)(2n)= 1/4？

b 1 = 1/4 b(n+ 1)/bn=( 1/4)^(n+ 1)/( 1/4？ )= 1/4

Sequence {bn} is a geometric series with 1/4 as the first term and 1/4 as the common ratio.

b 1+b2+...+bn =( 1/4)( 1- 1/4？ )/( 1- 1/4)=( 1/3)( 1- 1/4? )

n≥ 1，0 & lt； 1/4? ≤ 1/4 3/4≤ 1- 1/4? & lt 1 1/4≤( 1/3)( 1- 1/4? )& lt 1/3

1/m & lt； 1/4 m？ -6m + 16/3≥ 1/3

1/m & lt； 1/4m & lt； 0 or m> four

m？ -6m + 16/3≥ 1/3

m？ -6m +5≥0

(m-5)(m- 1)≥0

M≥5 or m≤ 1

To sum up, m is obtained.