Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

JUST wondering...

in binomial expansion can the general formula (a+b)^n ... blah blah blah be used to find coefficient up to a point and say the first 3 or 4 terms.??? i have been taught 2 different formulae and its completely messed my head up..can that general formula be used in all cases. thnx in advance :tongue:

:tongue:

What is the general formula as you understand it?

OP

pls 4give me i duno how to use latex but here we go:

(a+b)^n = a^n + (nchoose0)a^n + (nchoose1)a^n-1 X b + (nchoose2)a^n-2 X b^2

sorry tht looks sooo confusin bt hopefully u understnd

Not quite.

\displaystyle (a + b)^n = \begin{pmatrix} n \\ 0 \end{pmatrix} a^n + \begin{pmatrix} n \\ 1 \end{pmatrix} a^{n-1} b + \begin{pmatrix} n \\ 2 \end{pmatrix} a^{n-2} b^2 + \cdots + \begin{pmatrix} n \\ n \end{pmatrix} b^n

So you have an extra

a^n

at the beginning. However,

\displaystyle \begin{pmatrix} n \\ 0 \end{pmatrix} = \begin{pmatrix} n \\ n \end{pmatrix} = 1

, so you can just drop the coefficients of

a^n

and

b^n

if you find it easier to remember that way.

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