/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 62 What is true about the sum of th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 62

What is true about the sum of the exponents on \(a\) and \(b\) in any term in the expansion of \((a+b)^{n} ?\)

Short Answer

Expert verified
The sum of the exponents of \(a\) and \(b\) in any term of an expansion of \((a+b)^{n}\) is always \(n\)

Step by step solution

01

- Consider an arbitrary term in the expansion

Consider any term in the expansion of \((a+b)^{n}\) can be of the form \(a^{k}b^{(n-k)}\), where \(k\) is an integer, \(0 鈮� k 鈮� n\)
02

- Sum of exponents

Sum the exponents of \(a\) and \(b\) in this arbitary term which is \(k + (n - k)\)
03

- Simplify

Simplify \(k + (n - k)\). The \(k\) from \(n-k\) and \(k\) cancel out, yielding \(n\)
04

- Conclusion

Hence, the sum of the exponents of \(a\) and \(b\) in any term of the expansion \((a+b)^{n}\) is \(n\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If you toss a fair coin six times, what is the probability of getting all heads?

What is the difference between a geometric sequence and an infinite geometric series?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I toss a coin, the probability of getting heads or tails is 1 but the probability of getting heads and tails is \(0 .\)

You select a family with three children. If \(M\) represents a male child and \(F\) a female child, the sample space of equally likely outcomes is \(\\{M M M, M M F, M F M, M F F, F M M FMF, FFM, FFF\)} - Find the probability of selecting a family with $$\text{at least one male child.}$$

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises \(71-76\). A job pays a salary of \(\$ 24,000\) the first year. During the next 19 years, the salary increases by \(5 \%\) each year. What is the total lifetime salary over the 20 -year period? Round to the nearest dollar,
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.