1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Help with basic binomial coefficient

  1. Jan 19, 2017 #1
    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

    Hello. I'm currently working my way through Lang's Basic Mathematics and cannot make sense of this question:

    Show that if n is a positive integer at most equal to m, then

    [tex]{m \choose n}+{m\choose n-1}={m+1 \choose n}[/tex]


    The answer in the textbook is given as:

    1. [tex]{m \choose n}+{m\choose n-1}={m! \over n!(m-n)!}+{m! \over (m-n+1)!(n-1)}[/tex]

    [common denominator n!(m — n + 1)!]

    2. [tex]= {m!(m-n+1)+m!n\over n!(m-n+1)!}[/tex]

    I omitted the rest of the answer as I understand what follows from 2.

    However I don't understand how to get such denominator from 1.
    Could someone please help me?
    Last edited by a moderator: Jan 19, 2017
  2. jcsd
  3. Jan 19, 2017 #2


    User Avatar
    2017 Award

    Staff: Mentor

    I moved your thread to our homework section, as it is homework-like.

    In (1), you can write n! as n(n-1)! and (m-n+1)! as (m-n+1)(m-n)!. Afterwards the fractions should be easy to add with the usual methods.
  4. Jan 19, 2017 #3
    Thank you for the quick reply. This makes sense!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted