# Maths Power Series Watch

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How does one

'write down the 1st 4 terms of the power series for cos3x'????

can i use binomial or something?

'write down the 1st 4 terms of the power series for cos3x'????

can i use binomial or something?

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#2

I'm assuming that means it's a Taylor series:

f(a) + f'(a)x + (1/2!)f''(a)x^2 + (1/3!)f'''(a)x^3 + ...

where a is the point around which you're expanding the function. If you pick a = 0, the series is a MacLaurin's series.

f(a) + f'(a)x + (1/2!)f''(a)x^2 + (1/3!)f'''(a)x^3 + ...

where a is the point around which you're expanding the function. If you pick a = 0, the series is a MacLaurin's series.

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(Original post by

I'm assuming that means it's a Taylor series:

f(a) + f'(a)x + (1/2!)f''(a)x^2 + (1/3!)f'''(a)x^3 + ...

where a is the point around which you're expanding the function. If you pick a = 0, the series is a MacLaurin's series.

**Nylex**)I'm assuming that means it's a Taylor series:

f(a) + f'(a)x + (1/2!)f''(a)x^2 + (1/3!)f'''(a)x^3 + ...

where a is the point around which you're expanding the function. If you pick a = 0, the series is a MacLaurin's series.

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#4

(Original post by

so how would i use that for this cos3x?

**Ollie**)so how would i use that for this cos3x?

f'(x) = -3sin3x => f'(0) = 0

f''(x) = -9cos3x => f''(0) = -9

f'''(x) = 27sin3x => f'''(0) = 0

f''''(x) = (3^4)cos3x => f''''(0) = 3^4

I think you will find that you get:

1, 0, -3^2, 0, 3^4, 0, -3^6, 0, 3^8, ...

Sub this into the formula given:

cos3x = 1 - ((3^2)/2!)x^2 + ((3^4)/4!)x^4 - ((3^6)/6!)x^6 + ...

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(Original post by

f(x) = cos3x => f(0) = 1

f'(x) = -3sin3x => f'(0) = 0

f''(x) = -9cos3x => f''(0) = -9

f'''(x) = 27sin3x => f'''(0) = 0

f''''(x) = (3^4)cos3x => f''''(0) = 3^4

I think you will find that you get:

1, 0, -3^2, 0, 3^4, 0, -3^6, 0, 3^8, ...

Sub this into the formula given:

cos3x = 1 - ((3^2)/2!)x^2 + ((3^4)/4!)x^4 - ((3^6)/6!)x^6 + ...

**mikesgt2**)f(x) = cos3x => f(0) = 1

f'(x) = -3sin3x => f'(0) = 0

f''(x) = -9cos3x => f''(0) = -9

f'''(x) = 27sin3x => f'''(0) = 0

f''''(x) = (3^4)cos3x => f''''(0) = 3^4

I think you will find that you get:

1, 0, -3^2, 0, 3^4, 0, -3^6, 0, 3^8, ...

Sub this into the formula given:

cos3x = 1 - ((3^2)/2!)x^2 + ((3^4)/4!)x^4 - ((3^6)/6!)x^6 + ...

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#6

(Original post by

thanks very much

**Ollie**)thanks very much

http://www.nrich.maths.org.uk/askedN...ited/1282.html

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#7

okay...how advanced is this? AS, A2, Degree? Just interested...looks quite hard. I guess if you haven't learn it yet though then it would, heh.

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#8

Taylor/MacLaurin's series are covered in Edexcel's P6 (dunno in which module for other boards, but I guess either P5 or P6), so A Level Further Maths. I didn't do A Level Further Maths so I've only done them at uni (1st year Physics), but it doesn't seem that difficult to understand, involves lots of differentiation though.

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#10

(Original post by

Taylor/MacLaurin's series are covered in Edexcel's P6 (dunno in which module for other boards, but I guess either P5 or P6), so A Level Further Maths. I didn't do A Level Further Maths so I've only done them at uni (1st year Physics), but it doesn't seem that difficult to understand, involves lots of differentiation though.

**Nylex**)Taylor/MacLaurin's series are covered in Edexcel's P6 (dunno in which module for other boards, but I guess either P5 or P6), so A Level Further Maths. I didn't do A Level Further Maths so I've only done them at uni (1st year Physics), but it doesn't seem that difficult to understand, involves lots of differentiation though.

Ben

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#11

(Original post by

There are loads of clever methods for doing them - like for tan(x) and arctan(x) etc.

Ben

**Ben.S.**)There are loads of clever methods for doing them - like for tan(x) and arctan(x) etc.

Ben

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#12

(Original post by

pure 4 on OCR.

**fishpaste**)pure 4 on OCR.

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#13

(Original post by

Seems like people who do AQA A do MacLaurin's series in P3.

**Nylex**)Seems like people who do AQA A do MacLaurin's series in P3.

Ben

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#14

(Original post by

Yeah, but AQA A is weird. P3 is a further module, but P4 is not!

Ben

**Ben.S.**)Yeah, but AQA A is weird. P3 is a further module, but P4 is not!

Ben

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