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3 years ago

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Find an expression for the number of squares in the nth pattern of the sequence. I noticed that the number of squares you add in

each pattern it depends on the pattern number (see image) but I don't know how to get the expression.

1 answer:

Morgarella [4.7K]3 years ago

3 0

Answer:

make clear the question please

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)

notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true

Finally, if first step and second step are true, then the complete proposition is true.

So, given $2*n^3+3*n^2+n$

First step: using and replacing n=2 (the first valid integer number >1)

$2*(2)^3 +3*(2)^2+2=30$

$\frac{30}{6} =5$

As the result is an integer number, so the first step is true.

Second step: using any next number, $n+1$ , let it replace

$2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)$

As the First step is true, we know that

$2*n^3+3*n^2+n$ $=6*k$ ,

So let it replace in the previous expression

$6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]$

Finally

$\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)$

where the last expression is an integer number

So the second step is true, and the complete proposition is True

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3 years ago

Hey! i’ll give brainliest please help

Elan Coil [88]

Answer:

I would assume it to be the second option, or B.

'The bogs the moose lived in became so soggy that only moose with the largest feet could successfully walk on the bog'

Step-by-step explanation:

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klemol [59]

43% of 166 is 71.38 so it would be 71 to the nearest whole number!

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A hummingbird can make up to 150 flaps in 4 seconds. How long will it take for it to flap its wings 1000 times?

andreev551 [17]

1000/150 = 6 2/3 * 4 = 26 2/3 seconds

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3 years ago

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ch4aika [34]

Answer:

A, D, E

Step-by-step explanation:

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There are two points where the temperature reaches 74 degrees.

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