Question

write the formula for finding the rth term of the binomial (a+b)^n

Answer 1

\[(a+b)^n = \sum_{k=0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right)a^(n-k)b^k\]

Answer 2

a ^(n-k)

Answer 3

i do not know what that big E looking thing is,,,

Answer 4

fix that. it's not (n-k) *b^k. mistypo

Answer 5

it's the sum of some terms.

Answer 6

for example (a +b)^2 = a^2 +2ab +b^2 . it's the sum of 3 terms.

Answer 7

The big E is a capital S in Greek, the letter sigma. It stands for Sum.
which means add up each of the terms

Answer 8

ok

Answer 9

@phi: take care of him. thank you

Answer 10

\[ (a+b)^n = \sum_{k=0}^{n}\left(\begin{matrix}n \\ k\end{matrix}\right)a^{n-k}\ b^k \]

I am not sure what they mean by the rth term, but if we start counting from the highest order term, and call that 1, it would be
n choose 0 a^n b^0 = a^n

if you want the 2nd term it would be

n choose 1 a^(n-1) b^1

I think if you want the rth term, set k= r-1
in this formula.

n choose (r-1) a^(n-(r-1)) b^(r-1)

Answer 11

ok ty,,, i jusst don't get this

Answer 12

\[ \left(\begin{matrix}n \\ r-1\end{matrix}\right)a^{n-r+1}\ b^{r-1}\]

Answer 13

ty

Answer 14

If you have time, watch this
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/binomial_theorem/v/binomial-theorem--part-1

Answer 15

ty ty i will