### All Introduction to Analysis Resources

## Example Questions

### Example Question #1 : Power Series

Determine whether the following statement is true or false:

Some power series such as have a possible radius of convergence that can be found by computing the roots of the coefficients of .

**Possible Answers:**

True

False

**Correct answer:**

False

Explanation:

This statement is false because every power series has a radius of convergence that is found by computing the roots the series coefficients.

The proof of one case is as follows:

When is fixed, , and

with the assumption that and the Root Test is applied to the series .

When by the assumption and the notation that

implies that therefore by the Root Test, does not converge for any and thus the radius of convergence of is .

### All Introduction to Analysis Resources

Popular Subjects

Calculus Tutors in Houston, French Tutors in Phoenix, Algebra Tutors in Phoenix, GMAT Tutors in Philadelphia, Calculus Tutors in San Francisco-Bay Area, Chemistry Tutors in Miami, SAT Tutors in Washington DC, SAT Tutors in Denver, MCAT Tutors in Houston, Computer Science Tutors in Los Angeles
Popular Courses & Classes

GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, LSAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, GMAT Courses & Classes in Houston, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Seattle, GRE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Denver
Popular Test Prep

GMAT Test Prep in Denver, MCAT Test Prep in New York City, ISEE Test Prep in Washington DC, SSAT Test Prep in Denver, ACT Test Prep in Seattle, ISEE Test Prep in Philadelphia, GMAT Test Prep in Washington DC, GRE Test Prep in Phoenix, SAT Test Prep in Boston, GMAT Test Prep in San Diego