Binomial expansion

**gtaplayr** · August 8th 2009, 07:40 PM

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

**CaptainBlack** · August 8th 2009, 11:33 PM

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

**Jhevon** · August 8th 2009, 11:42 PM

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.

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