Function approaching... something
Let p be a function where for any positive x , p ( x ) is 7 x rounded up to the nearest whole number. Evaluate:
lim n → ∞ p n ( x )
Where x and n are both ANY positive number.
Details and Assumptions
- p n means p composed n times, or p ( p ( p ( p ( . . . x )
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1 solution
Hey buddy is it that p n ( x ) is p being composed n times? If that is so, you should've mentioned it buddy, I thought that it was raised to the power n .
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Yeah, I took a guess and luckily my first choice was p being composed n times, yeah it should be clarified
No, if you ever see a function raised to a power, it means a function of a function of a funtion n-times.
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It can also be such that it's being differentiated n times.
Finn did you have MathCounts States yesterday? How was it?
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No, it's in 2 weeks. But in advance I will tell you... Not great.;)
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What do you mean? :P
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@Stephen Shamaiengar – Oh, I'm saying that States is gonna suck. :D
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@Finn Hulse – Why, because you think a lot of the other people there are going to be better or more prepared? It is true, we experienced the same thing last year.
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@Stephen Shamaiengar – Yeah bro, there's Longfellow, Robert Frost, and a couple of other really good schools.
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@Finn Hulse – Don't forget Thomas Jefferson School for Science and Technology... I think some of those places have a MathCounts class. So they're always really good.
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@Stephen Shamaiengar – Oh yeah! I'm kind of scared out of my wits. Wouldn't it be awesome if I made it to Nationals?
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@Finn Hulse – Yea. I know you're good, but don't get your hopes up. When we went, Stas and Junha from Hornsby did get in the top 15 for the Countdown round but they were literally like 14 and 15 and they were eliminated in the first and second rounds.
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@Stephen Shamaiengar – Yeah, exactly.
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@Finn Hulse – Math Counts sounds really competitive in your states. In Idaho, we basically win every year for state because Idaho stinks. Nobody even tries, except for the schools that have people that throw their kids in a haguan.
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@Robert Fritz – Oh, it is. VA,TX, CA, and MA are the big 4. They always win.
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@Finn Hulse – Sounds usual.
You can try this with any number. All that this is asking is what value is always approached when you divide by 7, and round up, and divide by 7, etc. If we weren't rounding up, the answer would be 0. If we always rounded down, the answer would also be 0. But everything else is just to look fancy. The problem is just "What happens if you divide by 7 and round up to the nearest whole number infinite times.