Serge Lang - Basic Mathematics - Sum of Binomial coefficients p.387 ex. 9

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I can not understand the solution.How does the second step come about? How does the expression in brackets appear?

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asked Nov 20 at 8:13

Alexander Nikolin

$ab + ac = a[b+c]$ :-)
– trancelocation
Nov 20 at 8:16

yeah, I know, but here it is somehow not obvious to me
– Alexander Nikolin
Nov 20 at 8:20

add a comment |

up vote
0
down vote

favorite

I can not understand the solution.How does the second step come about? How does the expression in brackets appear?

solution image

asked Nov 20 at 8:13

Alexander Nikolin

$ab + ac = a[b+c]$ :-)
– trancelocation
Nov 20 at 8:16

yeah, I know, but here it is somehow not obvious to me
– Alexander Nikolin
Nov 20 at 8:20

add a comment |

up vote
0
down vote

favorite

I can not understand the solution.How does the second step come about? How does the expression in brackets appear?

solution image

asked Nov 20 at 8:13

Alexander Nikolin

I can not understand the solution.How does the second step come about? How does the expression in brackets appear?

solution image

binomial-coefficients

asked Nov 20 at 8:13

Alexander Nikolin

asked Nov 20 at 8:13

Alexander Nikolin

asked Nov 20 at 8:13

Alexander Nikolin

asked Nov 20 at 8:13

Alexander Nikolin

asked Nov 20 at 8:13

Alexander Nikolin

$ab + ac = a[b+c]$ :-)
– trancelocation
Nov 20 at 8:16

yeah, I know, but here it is somehow not obvious to me
– Alexander Nikolin
Nov 20 at 8:20

add a comment |

$ab + ac = a[b+c]$ :-)
– trancelocation
Nov 20 at 8:16

yeah, I know, but here it is somehow not obvious to me
– Alexander Nikolin
Nov 20 at 8:20

$ab + ac = a[b+c]$ :-)
– trancelocation
Nov 20 at 8:16

yeah, I know, but here it is somehow not obvious to me
– Alexander Nikolin
Nov 20 at 8:20

add a comment |

1 Answer
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Take note:

$$(n - k + 1)! = (n-k)! cdot (n - k + 1)$$

$$k! = (k-1)! cdot k$$

Rewrite the expression after the first equal sign with this in mind: you should see a common factor you can neatly factor out.

answered Nov 20 at 8:17

Eevee Trainer

1,474216

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

add a comment |

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
1
down vote

accepted

Take note:

$$(n - k + 1)! = (n-k)! cdot (n - k + 1)$$

$$k! = (k-1)! cdot k$$

Rewrite the expression after the first equal sign with this in mind: you should see a common factor you can neatly factor out.

answered Nov 20 at 8:17

Eevee Trainer

1,474216

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

add a comment |

up vote
1
down vote

accepted

Take note:

$$(n - k + 1)! = (n-k)! cdot (n - k + 1)$$

$$k! = (k-1)! cdot k$$

Rewrite the expression after the first equal sign with this in mind: you should see a common factor you can neatly factor out.

answered Nov 20 at 8:17

Eevee Trainer

1,474216

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

add a comment |

up vote
1
down vote

accepted

Take note:

$$(n - k + 1)! = (n-k)! cdot (n - k + 1)$$

$$k! = (k-1)! cdot k$$

Rewrite the expression after the first equal sign with this in mind: you should see a common factor you can neatly factor out.

answered Nov 20 at 8:17

Eevee Trainer

1,474216

Take note:

$$(n - k + 1)! = (n-k)! cdot (n - k + 1)$$

$$k! = (k-1)! cdot k$$

Rewrite the expression after the first equal sign with this in mind: you should see a common factor you can neatly factor out.

answered Nov 20 at 8:17

Eevee Trainer

1,474216

answered Nov 20 at 8:17

Eevee Trainer

1,474216

answered Nov 20 at 8:17

Eevee Trainer

1,474216

answered Nov 20 at 8:17

Eevee Trainer

1,474216

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

add a comment |

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

thanks! the problem was that the first property was not clear to me
– Alexander Nikolin
Nov 20 at 8:25

add a comment |

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