Chapter 10.5, Problem 64E

7. Use the binomial series to expand the function as a power series. State the radius of convergence. (a) VI- 8x (b) (1 – x)²/3 (c) 4+ x2

IV.) 1. Convergent or Divergent series will give upvote if correct

an -0 and Show that if lim %3D =1 n+ 00 converges thenEn=1 'n =1 converges too.

FIND THE TAYWR SERIES FUR f (x) = 7 ABOUT x=-3 X4

1, 0 ≤ x ≤ 1, 1. Find the Fourier sine series and Fourier cosine series for f(x) = on the lx+1, 1< x ≤2, interval [0,2]. Give the values of x in the interval [0,2] where we expect each series to converge nicely, and were we expect there to be trouble with convergence. Bonus: Display graphs of f(x) versus the graphs of the truncated versions of these Fourier series (use 200 terms) on [0,2] and comment on the behavior in each case.