# Binomial Theorem - small values of x and approximate values

1. Oct 15, 2005

### Bucky

"Show that for small values of x, the function (1+x)^(-1/2) may be approximated by

1-(1/2)x+(3/8)x^2

Hence obtain the approximate value of 1/root(1.01) to 4 decimals."

im totally clueless. the example we have isnt well explained at all. can someone even just start me off?

(incidentally what happened to the flex pluggin? i went to find it for the maths bits but cant find it)

2. Oct 15, 2005

### Tide

Just replace x with 0.01 in your binomial expansion and you will have the desired approximation.

3. Oct 15, 2005

### Bucky

what about the initial 'show that' bit?

4. Oct 15, 2005

### AKG

Do you know the binomial theorem?

5. Oct 15, 2005

### Bucky

(a+b)^n = a^n +na^(n-1)b + (n(n-1))/2! (etc) ....that one?

6. Oct 15, 2005

### Integral

Staff Emeritus
That's the one!

Now you have 1.01 , think of it as a+b where a=1 and b=.01.

Now, plug that into the binomial expansion, look at the magnitude of each monomial as you add them, continue until the terms are below your desired error.

7. Oct 15, 2005

### Bucky

ok thanks for your help guys..just one more question..

where did you get 1.01/0.01 from?

8. Oct 16, 2005

### HallsofIvy

Staff Emeritus
?? I don't see any reference to 1.01/0.01 in any of the previous responses!

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