Question

(9+1)^(1/2)
Find the first 4 terms of this using binomial expansion,

Answer 1

\[\sqrt{10}\]?

Answer 2

It's like (1/2)C0(a)^(1/2)(b)^(0) + (1/2)C1(a)^(-1/2)(b)^(1) and so on for 4 terms. I just don't know how to combine it.

Answer 3

oooh i see, maybe like
\[(1+9)^{\frac{1}{2}}=1+\frac{1}{2}\times 9+\frac{\frac{1}{2}\times -\frac{1}{2}}{2!}9^2+..\]

Answer 4

\[(1+a)^n=1+na+\frac{n(n-1)}{2!}a^2+\frac{n(n-1)(n-2)}{3!}a^3\]

if i remember it correctly

Answer 5

yes that is it i am sure (more or less) but because you are dealing with fractional exponent it goes on forever. and needs to look like
\[(1+x)^n\]

Answer 6

ummm. wut?

Answer 7

your going to have to be more specific than that ....

Answer 8

how did you get that string of numbers?

Answer 9

its the definition of a binomial expansion for rational exponents

Answer 10

im not quite sure how they come up with it yet, but i recall seeing it as such

Answer 11

that is not going to work for fractional exponents

Answer 12

read here for a brief explanation

Answer 13

\[\binom{n}{1}=\frac{n}{1!}\]
\[\binom{n}{2}=\frac{n(n-1)}{2!}\]
\[\binom{n}{3}=\frac{n(n-1)(n-2)}{3!}\]

etc...

Answer 14

those are textbook definitions i beleive

Answer 15

could you expand of (9+1)^(1/2) to 4 terms? I think that'd make more sense to me than just variables O_Ollll

Answer 16

satellite posted it above

Answer 17

4th post down