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

Question

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

$ab + ac = a[b+c]$ :-) – trancelocation Nov 20 '18 at 08:16 — trancelocation, Nov 20 '18 at 08:16
yeah, I know, but here it is somehow not obvious to me – Alexander Nikolin Nov 20 '18 at 08:20 — Alexander Nikolin, Nov 20 '18 at 08:20

score 1 · Accepted Answer · answered Nov 20 '18 at 08:17

1

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 '18 at 08:17

PrincessEev

thanks! the problem was that the first property was not clear to me – Alexander Nikolin Nov 20 '18 at 08:25

1 Answers1