Question

Evaluate each series. $$\sum_{i=1}^{4}\left[(-2)^{i}-3\right]$$

   Evaluate each series.
$$\sum_{i=1}^{4}\left[(-2)^{i}-3\right]$$

Precalculus

Margaret L. Lial,… 6th Edition

Chapter 11, Problem 52

Instant Answer

Solved by Expert Ankit Gupta

07/20/2020

Step 1

When $i=2$, we have $(-2)^2-3=4-3=1$. When $i=3$, we have $(-2)^3-3=-8-3=-11$. When $i=4$, we have $(-2)^4-3=16-3=13$. Now, let's add up these values: $(-5)+(1)+(-11)+(13)=-2$. Show more…

Show all steps

lock

Thanks for your feedback!

Evaluate each series. $$\sum_{i=1}^{4}\left[(-2)^{i}-3\right]$$

Play audio

Feedback

Powered by NumerAI

Ankit Gupta and 52 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Summation Notation

Summation notation is a compact way to represent the addition of a sequence of terms defined by an index that runs over a specified range. It provides a systematic approach to expressing finite or infinite sums and is foundational in understanding series and sequences.

Series Evaluation

Series evaluation involves calculating the total sum of all terms in a series, often by substituting specific values for the index and applying arithmetic operations systematically. This process helps in understanding patterns and behaviors in sequences of numbers.

Exponentiation with Negative Bases

Exponentiation with negative bases involves raising a negative number to a power. The outcome depends on whether the exponent is even or odd, with even exponents producing positive results and odd exponents retaining the negative sign. This concept is critical to accurately calculating terms in expressions involving powers.

Arithmetic Operations

Arithmetic operations, such as addition, subtraction, multiplication, and division, are the basic tools used to combine and simplify expressions in series. Mastery of these operations is essential for evaluating series and ensuring that each term is accurately calculated before summing them.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later