Thread: calculating the terms of a binomial expression

1. calculating the terms of a binomial expression

hello i have not done maths in a long time and need some help after a while reading some books and solving a few equations i have got stuck on the binomial expression (1+x)^1/2 i am trying to solve the first 5 terms.
i have expanded it i have no problems with that but my calculations to simplify the longer terms is a bit rusty i no the 4th term of the expression is:

+ (1/2)(1/2-1)(1/2-2)(x)^3 = i think 1/16x^3
3!

i have come up with this answer by looking at lots of examples and reading but i do not know if i am correct as i do not understand how to calculate or simplify the long term once i understand the basics of how a=b i will be able to solve more

2. Re: calculating the terms of a binomial expression

Yeah, that's fine.

3. Re: calculating the terms of a binomial expression

Yeah i thought that was correct but I would like to understand how to calculate the long term into the shortened term when I calculate it I do not get the shortened term if possible could someone demonstrate the calculation how (1/2)(1/2-1)(1/2-2)(x)^3 = 1/16x^3. Thanks olie 3!

4. Re: calculating the terms of a binomial expression

We have:

$\frac{\frac{1}{2}\cdot\frac{-1}{2}\cdot\frac{-3}{2}x^3}{3!}$

$=\frac{\frac{3}{8}x^3}{3\times{2}\times{1}}$

$=\frac{\frac{3}{8}x^3}{6}$

$=\frac{1}{16}x^3$

5. Re: calculating the terms of a binomial expression

thankyou so much i understand fully now it was the dividing by 3! that threw me off the target thanks again olie