
Exercise 51 illustrates that one of the nuances of “conditional� convergence is that the sum of a series that converges conditionally depends on the order that the terms of the series are summed. Absolutely convergent series are more depend- able, however. It can be proved that any series that is con- structed from an absolutely convergent series by rearranging the terms will also be absolutely convergent and has the same sum as the original series. Use this fact together with parts (a) and (b) of Theorem 9.4.3 in these exercises.
It was stated in Exercise 35 of Section 9.4 that π26=1+122+132+142+⋯
Use this to show that π28=1+132+152+172+⋯

Want to see the full answer?
Check out a sample textbook solution
Chapter 9 Solutions
Calculus: Early Transcendentals, Enhanced Etext
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (7th Edition)
College Algebra (7th Edition)
A First Course in Probability (10th Edition)
College Algebra with Modeling & Visualization (5th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
- Find all values of x for the given function where the tangent line is horizontal. 3 =√x³-12x² + 45x+5arrow_forwardFind the equation of the tangent line to the graph of the given function at the given value of x. 6 f(x) = x(x² - 4x+5)*; x=2arrow_forwardFind the equation of the tangent line to the graph of the given function at the given value of x. f(x)=√√x+33; x=4arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
