Ex 4


discrete-ucozfree.comematics proof-writing induction
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edited Jan 7, năm ngoái at 19:55
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asked Feb 2, 2013 at 13:08
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AndrewAndrew
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Your proof is fine, but you should show clearly how you got khổng lồ the last expression.

Bạn đang xem: Ex 4

$dfrack(k+1)(k+2)3+(k+1)(k+2)$

$=dfrack3(k+1)(k+2)+(k+1)(k+2)$

$=(dfrack3+1)(k+1)(k+2)$

$=dfrack+33(k+1)(k+2)$

$=dfrac(k+1)(k+2)(k+3)3$.

You should also word your proof clearly. For example, you can say "Let $P(n)$ be the statement ... $P(1)$ is true ... Assume $P(k)$ is true for some positive integer $k$ ... Then $P(k+1)$ is true ... Hence $P(n)$ is true for all positive integers $n$".


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edited Feb 2, 2013 at 16:55
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Michael Hardy
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answered Feb 2, 2013 at 13:15
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It might also be helpful to lớn go backwards to lớn see that it makes sense. Specifically, $$S_n+1 - S_n = frac(n+2)(n+1)(n)3 - frac(n+1)(n)(n-2)3 = frac13left(n^3 + 3n^2 + 2n - n^3 + n ight) = n(n+1)$$Going backwards, you can more easily see that $$S_n+1 = S_n + n(n+1)$$


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answered Mar 3, 2018 at 22:18
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kaiwenwkaiwenw
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