Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

In Exercises 101-104, prove the property for all integers $ r $ and $ n $ where $ 0 \le r \le n $.

$ _nC_r = _nC_{n - r} $

$\left(\frac{1}{x}+2 y\right)^{6}=\frac{1}{x^{6}}+\frac{12 y}{x^{5}}+\frac{60 y^{2}}{x^{4}}+\frac{160 y^{3}}{x^{3}}+\frac{240 y^{4}}{x^{2}}+\frac{192 y^{5}}{x}+64 y^{6}$

Calculus 2 / BC

Precalculus

Chapter 9

Sequences, Series, and Probability

Section 5

The Binomial Theorem

Series

Introduction to Sequences and Series

Introduction to Combinatorics and Probability

Campbell University

Idaho State University

Utica College

Lectures

04:22

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Many pairs of random variables are correlated, but in the absence of a causal relationship, this correlation is due to chance. For example, a study of the heights of parents and their children might show that pairs of individuals have a correlation of 0.7 for height, meaning that if the parent is 70 inches tall, the child is also on average 70 inches tall. This does not imply that parental height caused the child's height; both are usually caused by a common factor.

02:18

A sequence is a collection of objects in which repetitions are allowed. For example, the sequence (2, 4, 6, 8, 10) of even numbers can be written as {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, {2, 4, 6, 8, 10}, or any other of an infinite number of ways. The numbers in the sequence are called the terms of the sequence. The first number in the sequence is called the first term, the second number is called the second term, and so on. The nth term of a sequence is the number that is the nth member of the sequence. The kth term of a sequence is the number that is the kth member of the sequence.

03:01

In Exercises 101-104, p…

04:46

Proof In Exercises $99-102…

02:05

01:10

Prove the property for all…

00:49

101 Okay. This question or they have to do we have to just, uh, prove okay. This question. We have to just prove that these are the property regarding these Are the property. Okay for all Indigenous. Uh, that is an N R. Okay, so this is m. C arguing hair on had given NCR they should, because tow N C and menace are okay, so we'll check whether these are regular. Not so for that we're going to expand these two. Okay, So you will expand this to so that this is an factorial by and menace r factorial divided by, uh, our factory. Okay. Similarly, for this also right in factorial divided by and madness and menace r factorial And it is multiplied two and minus r factorial. We'll see whether electricity is equal strategies or not. So this will become manufacturer riel by end minus are territorial multiplied to r factorial. How If you see, this is an factorial by end minus and that becomes, uh, zero. And here it becomes manners are and manners that will become our okay. So it will become r factorial. I multiplied two and minus r factorial. Okay, social love this by attending this. Then we will find that alleges is recall strategist and factorial by Minister Factorial the plateau r factorial This is equals two and factorial by r factorial unnecessary to write in in the previous manner. That is an portrayal by and manage our pictorial on it is multiplied to alfa cooking. So from here, we can see that Alexis is equals to Are you Jess? So this is Yeah. We can see that this will satisfy the, uh, equation. Mental nutritionists. Correct. Our equation is colored. This is approved. Thank you.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:38

In Exercises 55-62, use the matrix capabilities of a graphing utility to eva…

01:14

In Exercises 7-16, use Cramer's Rule to solve (if possible) the system …

01:49

In Exercises 41 - 44, expand the binomial by using Pascals Triangle …

00:46

In how many ways can a $ 12 $-question true-false exam be answered?…

01:07

In Exercises 17-20, use a graphing utility and Cramer's Ruleto solve (i…

02:03

02:52

In Exercises 53 - 60, the sample spaces are large and you should u…

02:13

In Exercises 43 - 48, find a formula for the sum of the first $ n…

01:04

In Exercises 35 - 38, evaluate $ _nP_r $ using a graphing utility

00:19

In Exercises 101-104, evaluate the determinant.

$\left| \begin{array…