Math 116
Jeff Mermin’s section
Extra Credit homework 11: Convergence of Power Series
To have this assignment graded, you must have done a satisfactory job on
Extra Credit homework 9 and 10.
You can use the ratio test or the root test to answer all of these questions.
You may also be able to identify a metatheorem or two. Your answer should be
an interval.
1. At what xdoes the power series for exconverge?
2. At what xdoes the power series for sinxconverge?
3. At what xdoes the power series for cosxconverge?
4. At what xdoes the power series for ln(1 + x) converge?
5. At what xdoes the power series for 1
1+xconverge?
6. At what xdoes the power series for 1
1+x2converge?
7. At what xdoes the power series for arctanxconverge?