Hey guys, I was just wondering if any of you have any thoughts on this problem. I've exhausted all mine

Let's say we have 2 functions: f and g with and .

Then define two sequences:

1) = 3 and = for n 1

2) = 100 and = for n 1

What is the smallest positive integer m for which ?

I've tried connecting the two series with an inequality but I can't quite get one that I can prove. I've probably overlooked something blindingly obvious

Thanks in advance if you guys can help