;; = the minimum value of all n held by m \"Understanding this sentence clearly is the key to this problem! Now that we know that the language is difficult to un" />
"bm is the lowest!" , "bm is the minimum value of all n!" , "bm is the minimum value of all n held by inequality an>= m!" So you can see clearly!
So the key to solve the problem now is to find the inequality an>, and all n =m holds. Substitute the general formula an=2n- 1 into the inequality and get: 2n-1>; =m,( 1)
Finishing: n & gt=(m+ 1)/2, (2)
That is to say, bn is the minimum value of n in formula (2)!
M is a positive integer, so m takes 1, 2, 3 and 4 in turn. . . . . . The minimum value of n can be obtained. Considering that n is also the cornerstone of an and can only be an integer, bn sequence can be obtained:
b 1= 1,b2=2,b3=2,b4=3,b5=3。 . . . . . Namely:
Bn=(n+ 1)/2, when n is odd;
=(n+2)/2, when n is even.