/*! 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 35 Find each indicated sum. $$\su... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 35

Find each indicated sum. $$\sum_{i=1}^{4}\left(-\frac{1}{2}\right)^{i}$$

Short Answer

Expert verified
The sum of the geometric series is \( -\frac{15}{32} \).

Step by step solution

01

Identify necessary elements

In the given series \( \sum_{i=1}^{4}\left(-\frac{1}{2}\right)^{i} \), the first term \( a \), can be found by substituting \( i = 1 \) i.e., \( a = (-\frac{1}{2})^{1} = -\frac{1}{2} \). The common ratio \( r = -\frac{1}{2} \) and the number of terms \( n = 4 \).
02

Use the geometric sequence sum formula

Substitute \( a = -\frac{1}{2} \), \( r = -\frac{1}{2} \) and \( n = 4 \) into the geometric sequence sum formula \( S = a * \frac{1 - r^n}{1 - r} \).
03

Calculate the sum

Input values into the equation gives us: \( S = -\frac{1}{2} \times \frac{1 - (-\frac{1}{2})^{4}}{1 - -\frac{1}{2}} \). Solving gives: \( S = -\frac{1}{2} \times \frac{1 - \frac{1}{16}}{1.5} = -\frac{15}{32} \)

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

Which one of the following is true? a. \(\frac{n !}{(n-1) !}=\frac{1}{n-1}\) b. The Fibonacei sequence \(1,1,2,3,5,8,13,21,34,55,89\) \(144, \ldots\) can be defined recursively using \(a_{0}=1, a_{1}=1\) \(a_{n}=a_{n-2}+a_{n-1},\) where \(n \geq 2\). c. \(\sum_{i=1}^{2}(-1)^{i} 2^{i}=0\) d. \(\sum_{i=1}^{2} a_{i} b_{i}=\sum_{i=1}^{2} a_{i} \sum_{i=1}^{2} b_{i}\)

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (2 x+1)^{4} $$

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

Find the term in the expansion of \(\left(x^{2}+y^{2}\right)^{5}\) containing \(x^{4}\) as a factor.

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

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.