Understanding the Simplification of Binomial Coefficients

[BMY61]

Here is the problem i am having trouble:

Expressing the binomial coefficients in terms of factorials and simplifying algebraically show that

(n over r) = (n-2+1)/r (n over r-1)

i got that equals ((n-r+1)/r) ((n!)/((r-1)!(n-(r-1))!)) but i am trying to get that to equal n!/r!(n-r)! which would bring me back to (n over r)

i am just getting confused on what to all do in between.
hope i did no confuse anyone

 

[mathman]

Here is the problem i am having trouble:

Expressing the binomial coefficients in terms of factorials and simplifying algebraically show that

(n over r) = (n-2+1)/r (n over r-1)

i got that equals ((n-r+1)/r) ((n!)/((r-1)!(n-(r-1))!)) but i am trying to get that to equal n!/r!(n-r)! which would bring me back to (n over r)

i am just getting confused on what to all do in between.
hope i did no confuse anyone

I believe you have an error in the statement. The right hand side should read:
(n-r+1)/r (n over r-1). However, you seem to have the next statement correct.

To get the final result, note that r(r-1)! = r!
Also (n-(r-1))!=(n-r+1)!=(n-r+1)(n-r)!

 

[BMY61]

ahh ok, thank you