Purchase Solution

# Recursive relationships

Not what you're looking for?

Consider the recursive relationship for combinations:

C(n,r) = C(n-1,r) + C(n-1,r-1)

Prove this relationship algebraically using the mathematical definition of a combination, as well as that of the factorial function.

Provide a logical explanation for this relationship (Hint: consider n objects as consisting of n-1 existing objects plus a new nth object. Given the ultimate goal of selecting r objects from the entire set of n, you must select objects from the set of n-1 objects and decide how the new nth object should join the existing selected sets.)

##### Solution Summary

This solution shows a simple proof regarding recursive relationships. It is solved in step by step format.

##### Solution Preview

Because, C(n,r) = n!/(r!*(n-r)!)
RHS:
C(n-1,r) + C(n-1,r-1)
= {(n-1)!/(r!*(n-1-r)!)} + {(n-1)!/((r-1)!*(n-r)!}
= {(n-1)!/((r-1)!*(n-r-1)!)} * { (1/r) + (1/(n-r))}
(Because, (n-r)! = (n-r-1)!*(n-r); r! = (r-1)!*r)

= {(n-1)!/((r-1)!*(n-r-1)!)} * {(n-r + ...

Solution provided by:
###### Education
• MSc , Pune University, India
• PhD (IP), Pune University, India
###### Recent Feedback
• " In question 2, you incorrectly add in the \$3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
• "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
• "Great thanks"
• "Perfect solution..thank you"

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts