La Derive Newton's iden tity() in termsb.) Use part ca) toitsofexpressDIeredecessor

To prove nkkr=nrn-rk-r , n≥k≥0 L.H.S…

Answered: 1)a Derive Newton's iden tity b.) Use…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 47E

See similar textbooks

Related questions

Question

La Derive Newton's iden tity
() in terms
b.) Use part ca) to
its
of
express
DIeredecessor

Expert Solution

part a

To prove $(\begin{matrix} n \\ k \end{matrix}) (\begin{matrix} k \\ r \end{matrix}) = (\begin{matrix} n \\ r \end{matrix}) (\begin{matrix} n - r \\ k - r \end{matrix}), n \geq k \geq 0$

L.H.S

$\begin{array}{rcl} (\begin{matrix} n \\ k \end{matrix}) (\begin{matrix} k \\ r \end{matrix}) & = & \frac{n!}{k! (n - k)!} \frac{k!}{r! (k - r)!} \\ = & \frac{n!}{r! (n - k)! (k - r)!} \\ = & \frac{n!}{r! (n - r)!} \frac{(n - r)!}{(n - k)! (k - r)!} \\ = & \frac{n!}{r! (n - r)!} \frac{(n - r)!}{(k - r)! [(n - r) - (k - r)]!} \\ = & (\begin{matrix} n \\ r \end{matrix}) (\begin{matrix} n - r \\ k - r \end{matrix}) \\ R . H . S \end{array}$

Hence proved.

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

1)a Derive Newton's iden tity b.) Use part ca) to express its () in terms for predecessor. n-ktl