Fractions and Decimals

Discrete Mathematics

Differential Equations

Diagram & Picture

Numbers & Operations

Data & Statistics

Natural Numbers

Ratios & Proportions

Order of Operations

Exponents & Radicals

Complex Numbers

Congruence & Similarity

Pythagorean Theorem

Transformations

Data Collection & Representation

Measures of Central Tendency

Measures of Spread

Statistical Inference

Non-Right Triangle

Unit Circle & Radians

Identities & Equations

Limits & Continuity

Sequences & Series

Solved on Nov 27, 2023

Find the center of the power series $\sum x^n / n^3$ . The options are: a) 2, b) 3, c) $1/2$ , d) -1, e) $-1/2$ , f) -1, g) 1, h) -3, i) 0.

STEP 1

Assumptions1. The power series is given by $\sum x^{\wedge} n / n^{\wedge}3$ . . We are asked to find the center of this power series.

STEP 2

The center of a power series is the value of $x$ where the series is centered. In other words, it's the value of $x$ that makes the series converge to a finite value.

STEP 3

For a power series of the form $\sum a_n (x - c)^n$ , the center of the series is $c$ .

STEP 4

In our case, the power series is given by $\sum x^{\wedge} n / n^{\wedge}3$ . This can be rewritten as $\sum (x -0)^n / n^{\wedge}3$ .

STEP 5

Comparing this with the general form of the power series, we can see that the center $c$ is0.
Therefore, the center of the power series $\sum x^{\wedge} n / n^{\wedge}3$ is0.

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms