a 4 points Using the geometric series obtain a power series with center c 0 for

A 4 points using the geometric series obtain a power

This preview shows page 11 - 13 out of 14 pages.

7.(a) (4 points) Using the geometric series, obtain a power series with centerc= 0 for the function1x+ 1.(b) (4 points) Using the properties of derivatives and integrals of power series, find a power series withcenterc= 0 forln(1 +x2).Be sure to state the radius of convergence in both cases carefully, and to justify your choice ofintegration constant if necessary. Solution:
UCLA: Math 31B Final exam (practice) (solutions) Spring, 2017 8.(a) (3 points) Does the seriesXn=014n2-1converge? Justify your answer carefully.(b) (7 points) Evaluate the series above.Hint:use the definition of the series as a limit of partialsums. Calculate the partial sum by first using partial fractions. Solution:

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture