- #1

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**Given that the sum of the geometric series is:**

1+x+x^(2)+x^(3)+x^(4)....=1/1-x for -1<x<1

**Find power series for**

1/1+x

**Not to sure where to start, any help would be great**

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- Thread starter andrey21
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- #1

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1+x+x^(2)+x^(3)+x^(4)....=1/1-x for -1<x<1

1/1+x

- #2

tiny-tim

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(try using the X

1+x+x^(2)+x^(3)+x^(4)....=1/1-x for -1<x<1

come

- #3

- 466

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Find the power series of:

3/2-x

Any help would be great

- #4

tiny-tim

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:rofl: I realised after posting the question how easy it actally is.

he he

3/2-x

3/2 1/(1- x/2)

- #5

Mark44

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This one is very easy. The power series of 3/2 - x is... 3/2 - x.:rofl: I realised after posting the question how easy it actally is. I do have a slightly harder one I am having trouble with:

Find the power series of:

3/2-x

On the offchance that you really meant 3/(2 - x), see tiny-tim's post.

- #6

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3/(2-x) = 3/2 + 3/2x + 9/4 x^2 + 27/8 x^3 + 81/16 x^4 + .....

Is this correct??

- #7

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What is wrong in your series is that when you create it you have to leave the 3/2 outside the 1/(1-x/2), expand the 1/(1-x/2) using the power series for 1/(1-x) and put x/2 in all the places where there is x in the power series, then multiply 3/2 into the series.

- #8

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Expansion of 1/(1-x/2) = 1+ x/2 + x

Now multiplying by 3/2 gives:

3/2 + 3x/4 + 3x

- #9

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That should be correct.

- #10

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Thanks ojs

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