Paper III 2015

Question 5

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For the second part of Q5, I did it slightly differently to the mark scheme. I want to ask if I'd still get credit.
In a similar manner to the integral maths solutions I said that 2^(1/3) and 2^(2/3) were either both rational or both irrational (from earlier), so set out only to prove the former was irrational.

So I said:

Question 7

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During question 7, I proved the result $Dn( x^a) = a^n * x^a $(by induction) and then continued to use this throughout.

Is the follow logic valid?

Let $u = (1-x) \Rightarrow du=-dx$
So $Dn(1-x)^m = (-1)^n * Dnu^m = (-1)^n * Dnu^m = (-1)^n * m^n * (1-x)^m$
Hence the expression is divisible by $(1-x)^{m-n}$

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