# Some kind of mathematical formula that I obviously dont know about?

1. Nov 29, 2011

### M. next

Hello there.
Can you please explain the following:
Let us suppose that δ is very much less than r, and expand |r+δ|^-1 in powers of δ/r. Keeping the lower order terms gives:
|r+δ|^-1 ≈ 1/r.(1-r.δ/r^2) + 1/2r [3(δ.r/r)^2-(δ/r)^2]

How did they reach here? is this kind of a mathematical formula that i dont know about?

2. Nov 29, 2011

### rlewit

I don't know that your aproximation is correct? If I set δ = 0 then the equation becomes

1/|r| ≈ 1/r

That doesn't look right?

3. Nov 29, 2011

### mathman

|r+δ| = |r||1+δ/r|. Since δ/r << 1, you may use |r|(1+δ/r).

Take the reciprocal and expand (1+δ/r)-1 in a power series.

4. Nov 29, 2011

### M. next

What do you exactly mean by a power series, mathman?

5. Nov 30, 2011

### Staff: Mentor

See the binomial series, and use just the first few terms, since they diminish rapidly for d/r very much smaller than 1: http://mathworld.wolfram.com/BinomialSeries.html

6. Nov 30, 2011

### Staff: Mentor

I would check the approximation formula that you quote, too. That is, evaluate it for a small delta/r, say, .0015, and verify that it gives a good approximation. (Otherwise you might be futilely trying to arrive at a formula that you have transcribed wrongly. I haven't checked it.)

7. Nov 30, 2011

### M. next

Thank you, NascentOxygen. I get it now. :)

8. Nov 30, 2011

### mathman

(1+x)-1 = 1 - x + x2 - x3 + x4 - ....

Formula holds for |x| < 1.

9. Dec 1, 2011

### M. next

Thank you.

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