/*! 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 125 Determine whether the statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 125

Determine whether the statement is true or false. Justify your answer. $$\sum_{i=1}^{4}\left(i^{2}+2 i\right)=\sum_{i=1}^{4} i^{2}+2 \sum_{i=1}^{4} i$$

Short Answer

Expert verified
The statement is true.

Step by step solution

01

Calculate left-hand side

Start by evaluating the left-hand side of the equation, which is the sum of \((i^{2}+2i)\) from i=1 to 4. Iterate over each integer from 1 to 4, plug it into the expression, and then add up the resulting values: \((1^2+2*1)+(2^2+2*2)+(3^2+2*3)+(4^2+2*4) = 3+8+15+24 = 50.
02

Calculate right-hand side

Next, calculate the right-hand side of the equation, which is given as the sum of \(i^{2}\) from i=1 to 4 plus twice the sum of \(i\) from i=1 to 4. As in the previous step, iterate over each integer from 1 to 4, plug it into both expressions, and then add up the resulting values: \((1^2+2^2+3^2+4^2) + 2*(1+2+3+4) = 30 + 20 = 50.
03

Compare both sides

Now that the values on both sides are computed, compare them to determine whether the original statement is true or false. Since the calculated result is 50 for both sides, the statement is true.

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

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{(-1)^{2 n+1}}{(2 n+1) !}$$

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$0,3,8,15,24, \ldots$$

Use the Binomial Theorem to expand and simplify the expression. \((2 x-y)^{5}\)

Write the first five terms of the sequence defined recursively. Use the pattern to write the \(n\) th term of the sequence as a function of \(n .\) (Assume \(n\) begins with 1.) $$a_{1}=25, a_{k+1}=a_{k}-5$$

Use the Binomial Theorem to expand and simplify the expression. \((4 x-3 y)^{4}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

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.