Skip to main content
Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 45
Chapter 9, Problem 45

Express each sum using summation notation. Use 11 as the lower limit of summation and ii for the index of summation. 2+22+23+⋯+2112+2^2+2^3+\(\cdots\)+2^{11}

Verified step by step guidance
1
Identify the pattern in the sum: the terms are powers of 2 starting from 2^1 up to 2^{11}.
Recognize that the index of summation, i, will represent the exponent on 2 in each term.
Set the lower limit of summation to 1, since the first term is 2^1.
Set the upper limit of summation to 11, since the last term is 2^{11}.
Write the summation notation as \(\sum_{i=1}^{11} 2^{i}\) to represent the entire sum.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Summation Notation

Summation notation is a concise way to represent the sum of a sequence of terms using the sigma symbol (∑). It includes an index of summation, lower and upper limits, and a general term formula. For example, ∑ from i=1 to n of a_i represents adding terms a_1 through a_n.
Recommended video:
05:18
Interval Notation

Exponents and Powers

Exponents indicate repeated multiplication of a base number. For instance, 2^3 means 2 multiplied by itself three times (2×2×2=8). Understanding how to express terms with exponents is essential when writing sums involving powers in summation notation.
Recommended video:
04:10
Powers of i

Index of Summation and Limits

The index of summation (commonly i) represents the variable that changes in each term of the sum. The lower limit is the starting value of i, and the upper limit is the ending value. Correctly setting these limits ensures the sum includes all intended terms.
Recommended video:
Guided course
03:50
Adding & Subtracting Like Radicals
Related Practice
Textbook Question

Express each repeating decimal as a fraction in lowest terms. 0.5‾=510+5100+51000+510,000+⋯0.\(\overline{5}\)=\(\frac{5}{10}\)+\(\frac{5}{100}\)+\(\frac{5}{1000}\)+\(\frac{5}{10,000}\)+\(\cdots\)

Textbook Question

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

∑i=117(5i+3)\(\sum\)_{i=1}^{17} (5i + 3)

Textbook Question

Find the sum of the even integers between 21 and 45.

3
views
Textbook Question

In Exercises 45-46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 6.

5
views
Textbook Question

Find the term indicated in each expansion. (x − 1/2)9; fourth term

Textbook Question

Find the sum of the odd integers between 30 and 54.