{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# L8W09 - MATH 135 Winter 2009 Lecture VIII Notes Binomial...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 135 Winter 2009 Lecture VIII Notes Binomial Theorem Recall that we are trying to come up with a way of expanding ( a + b ) n without actually having to expand it for each value of n in which we are interested. This is similar to wanting to come up with “closed form” expressions for things like 1 2 + 2 2 + ··· + n 2 . Last time we introduced the notation n r = n ! r !( n- r )! and did a few calculations. Binomial Theorem (Theorem 4.34) If a and b are any numbers and n ∈ P , then ( a + b ) n = n a n + n 1 a n- 1 b + ··· + n r a n- r b r + ··· + n n- 1 ab n- 1 + n n b n Alternatively, we can write ( a + b ) n = n X r =0 n r a n- r b r . We will prove this and do some calculations, but need to do look at a couple of preliminary re- sults first. Proposition 4.33 If n and r are integers with 0 ≤ r ≤ n , then n r is an integer. Rationale We will not formally prove this. However, last time we looked at n r as the number of ways of choosing r objects from among n objects. Since this number of ways is an integer, then n r should be an integer.be an integer....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

L8W09 - MATH 135 Winter 2009 Lecture VIII Notes Binomial...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online