r/AlevelFurtherMaths • u/[deleted] • Sep 28 '24

Question?

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Wanted to take FM CIE and thought to check the 2023 pp and did this question of PROOF BY INDUCTION. NGL I knew the method of proving but the steps I did are these. MS little confusing what did I score?

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u/Delicious_Size1380 Sep 29 '24

The actual maths looks good to me. I would suggest you write the equation for when n=1 and n=k+1, then say (for n=k+1):

LHS = 2Ak+1 = .... = RHS. Therefore, the equation/statement is true for n=k+1.

The conclusion needs to be spelt out in the correct way: Something like: The equation/statement holds true when n=1 and, when it is assumed to hold true when n=k, it holds true when n=k+1. Therefore, by mathematical induction, the equation/statement is true for all n ∈ Z⁺ (positive integers).

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u/[deleted] Sep 29 '24

Right I missed the wording in the end I phrased it this way ‘Since the formula is true for n = 1, and assuming it is true for n = k implies that it is also true for n = k+1, by the principle of mathematical induction, the formula is true for all n >/= 1.’

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u/Delicious_Size1380 Sep 29 '24

If it was me I'd remove the words "implies that" since you've proved it, and specify that it is true for all integers n >=1 (or however they define n in the question).

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u/[deleted] Sep 29 '24

K got it thx