(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

The mark scheme is 2, 2, 3, 3

For a) ii), it's a sequence of integers up to the floor of n^{2}/2

3. The attempt at a solution

We haven't done growth rates of sequences, only of equations. a) i) looks like the growth rate would be 5^{n}, but I don't know how to show the calculation of that

a) ii) difference between the differences is one, so there's an n^{2}in the term equation. That's all I can figure out.. it seems a bit trivial but would I plug in n^{2}to the final term, getting a quartic growth? How would I explain this properly to answer the question?

b) i) f(n) > 0, and I get to the point of showing that the equations for n=3 and n=4 etc have x_{n}gives a sum of f and previous x_{n}values, making the result have a majority of positives ( f(n) >0 ) but I'm having trouble showing that this is true for all n, mathematically. I can't just say "as n continues, the value for x > 0 since it's a sum of f(n) values, which are all positive" after only writing the value of x_{3}and x_{4}. Also, I don't think this is true. I need to be able to show that this is a positively growing function. I don't know if the sequence of numbers in f(n) is increasing or decreasing either

b) ii) The function part is replaced by the root and the n5^{n}, and again, we haven't done growth rates of sequences in class, only of equations. Do I turn this into a explicit form of the sequence? We haven't worked with fractional powers, so I don't know how to approach this method either. Our classes are really unfair: metaphorically; they expect us to write essays only after knowing the alphabet, no grammar is taught.

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# Homework Help: Growth rates and induction

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