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    In my 9231 Further maths syllabus, on mathematical induction it says -

    recognise situations where conjecture based on a limited trial followed by inductive proof is a useful strategy, and carry this out in simple cases e.g. find the nth derivative of x(e^x).

    If we try to do this for x(e^x), first we will differtiate it a couple of times and find the pattern and than finally prove the guess with induction. Am I correct or is their another way?
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    (Original post by Rishabh95)
    In my 9231 Further maths syllabus, on mathematical induction it says -

    recognise situations where conjecture based on a limited trial followed by inductive proof is a useful strategy, and carry this out in simple cases e.g. find the nth derivative of x(e^x).

    If we try to do this for x(e^x), first we will differtiate it a couple of times and find the pattern and than finally prove the guess with induction. Am I correct or is their another way?
    Yes, you're right. The idea is that if you do something recursively a few times and spot a pattern, then you can make a conjecture about the nth recursion and then prove that it's true by induction.
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    (Original post by nuodai)
    Yes, you're right. The idea is that if you do something recursively a few times and spot a pattern, then you can make a conjecture about the nth recursion and then prove that it's true by induction.
    Thanks for the help!
 
 
 
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