Let b1=1 and bn=1+[1/(1+bn-1)] for all n≥2. Note that bn≥1 for all n in N (set of all positive integers).
The Attempt at a Solution
Prove that (b2k-1)k in N
By definition, a sequence (an) is increasing if an≤an+1 for all n in N.
SO, for this problem, must prove b2n-1≤b2n for all n.
Proceed by induction:
Start with n=1.
b1=1 and b2=3/2, so
Assume inductively that b2n-1≤b2n, prove b2n≤b2n+1
Am I doing this correctly? I want to know before I continue.