/*! 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 59 Express each sum using summation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 59

Express each sum using summation notation. Use a lower limit of summation of your choice and \(k\) for the index of summation. $$a+(a+d)+(a+2 d)+\dots+(a+n d)$$

Short Answer

Expert verified
The sum can be expressed in summation notation as \(\sum_{k=0}^{n} (a+kd)\).

Step by step solution

01

Identify the pattern in the sequence

In the given sequence \(a+(a+d)+(a+2 d)+\dots+(a+n d)\), the first term is 'a'. Successive terms are incrementing by the common difference 'd'.
02

Express in summation notation

Using summation notation, the series can be written as \(\sum_{k=0}^{n} (a+kd)\). Here, 'k' is the index of summation which starts from 0 and goes up to 'n'. The summand '(a+kd)' represents the terms in the series, with 'k' multiplied by the common difference 'd' and 'a' being the first term.

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 \(f(x)=x^{5},\) find \(\frac{f(x+h)-f(x)}{h}\) and simplify.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x-1)^{5} $$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (4 x-1)^{3} $$

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(y^{3}-1\right)^{20} $$

Find the term indicated in each expansion. \(\left(x^{3}+y^{2}\right)^{8} ;\) sixth term
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.