# Binomial expansion

• Aug 8th 2009, 08:40 PM
gtaplayr
Binomial expansion
From the binomial expansion theorem there are terms in
$x^{k+1}$, $x^ky$, ...... , $xy^k$, $y^{k+1}$.
What are the coefficients of the general term $x^ry^{k+1-r}$ for:
i) r = 0
ii) r = 1,.....,k
iii) r = k + 1
• Aug 9th 2009, 12:33 AM
CaptainBlack
Quote:

Originally Posted by gtaplayr
From the binomial expansion theorem there are terms in
$x^{k+1}$, $x^ky$, ...... , $xy^k$, $y^{k+1}$.
What are the coefficients of the general term $x^ry^{k+1-r}$ for:
i) r = 0
ii) r = 1,.....,k
iii) r = k + 1

See the Mathworld or the Wikipedia Article

CB
• Aug 9th 2009, 12:42 AM
Jhevon
Quote:

Originally Posted by gtaplayr
From the binomial expansion theorem there are terms in
$x^{k+1}$, $x^ky$, ...... , $xy^k$, $y^{k+1}$.
What are the coefficients of the general term $x^ry^{k+1-r}$ for:
i) r = 0
ii) r = 1,.....,k
iii) r = k + 1

It seems you are using the definition: $(x + y)^{k + 1} = \sum_{r = 0}^{k + 1} {k + 1 \choose r}x^ry^{k + 1 - r}$.

now just plug in the respective $r$'s and you will be able to find the coefficients.