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sattari [20]
3 years ago
14

Prove that for all n in the naturals, n(n+1)(n+2) is divisible by 3

Mathematics
1 answer:
DerKrebs [107]3 years ago
6 0
By induction:

It's true for n=1, since 1\cdot2\cdot3 clearly contains a factor of 3.

Suppose it's true for n=k, that k(k+1)(k+2) is divisible by 3. Then

(k+1)(k+2)(k+3)=\dfrac{k(k+1)(k+2)(k+3)}k=\dfrac{3m(k+3)}k

where m is an integer. This reduces to

\dfrac{3m(k+3)}k=3m+9\dfrac mk

and both terms are clearly multiples of 3. We know that \dfrac mk is an integer since we had set m=k(k+1)(k+2) previously, which implies m is a multiple of k. So the statement is true.
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3 years ago
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Tems11 [23]

Answer:

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Step-by-step explanation:

Given

6x² - 3x - 30 ← factor out 3 from each term

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Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

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Use these factors to split the x- term

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6x² - 3x - 30

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3 years ago
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vovikov84 [41]

Answer:

<h2>18 + 45m</h2>

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The distributive property: a(b + c) = ab + ac

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3 years ago
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2^-3

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3 years ago
Read 2 more answers
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