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?

solution image

Answer 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.