A) \[a(100)\le 100\]
B) \[a(100)>100\]
C) \[a(200)\le 100\]
D) \[a(200)<100\]
Correct Answer: A
Solution :
[a] It can be proved with the help of mathematical induction that \[\frac{n}{2}>a(n)\le n.\] \[\therefore \,\,\,\,\frac{200}{2}<a(200)\] \[\Rightarrow a(200)>100\] and \[a(100)\le 100.\]
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