Convergence parameter Find the values of the parameter p > 0 for which the following series converge.
75.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Glencoe Math Accelerated, Student Edition
- Does the series (showing the picture) converge or diverge? Choose the correct answer below. 1) The integral test shows that the series converges 2) The nth-term test shows that the series converges 3) The series diverges because the series is a geometric series with |r|>=1 4) The nth-term test shows that the series divergesarrow_forwardFpr the convergent series from 1 to infinity of ((-1)^k*k)/(k^2+1), what is the value of the series with a remainer less than 10^-3 (an estimate)arrow_forwardNumerical Methods Use 5 decimal place mantissa. Approximate the following functions using Taylor series. Solve the absolute and relative error in each item when x = 3(Answer Problem No.1)arrow_forward
- Using power series with integration to find the length of x^2/a^2+y^2/b^2=1. assume b>0. Solution hint as below: consider there two case(a>b, or a<b) with different solution Set x=acosu,y=bsintu,0<=u<=2pi, L=integral(2pi,0()sqrt((dx/du)^2+(dy/dt)^2)dtarrow_forwarda) Find the series’s radius and interval of convergence. Then identify the values of x for which the series converges b) absolutely and c) conditionally.arrow_forwardSigma k=1 to infinity -20*8^k/4*9^k series converges or diverges. show stepsarrow_forward
- 2. Find the interval of convergence for the Maclaurin series for the function of f(x)= sin(x) a) Find the Maclaurin series for sin(x): b) Apply the Ratio Test: (Form the fraction |an+1| / |an| and simplify as much as possible) c) Evaluate the limit: d) Find the interval of convergence: HINT: Recall that the limit needs to be less than 1arrow_forward(a) find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) absolutely and (c) conditionally.arrow_forward(a) find the series’ radius and interval of convergence.Then identify the values of x for which the series converges(b) absolutely and (c) conditionally.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning