Help with calculus. infinite series, ratio test, etc.?
okay so i am doing my homework and i'm not sure how to do some of the problems.
1. Write out the first four terms of the series (-1)^(n+1)(1/n)*(x/3)^n. Terms do not need to be simplified. (Is that x supposed to be an n?)
2. Showing your work use the ratio test to start finding the interval of convergence for the series (the series above). Do everything except check the endpoints.
3. Now check the endpoints.
4. Find an infinite series for f(x)= sin(x^5). Write out the first four terms, simplifying as much as possible.
5. Find an infinite series for f(x)= x^3*sin(x^5). Write out the first four terms, simplifying as much as possible.
6. Does the series 1/n^2 converge? Explain briefly.
Sorry to ask so many questions! Any and all help on any of the questions is greatly appreciated!