1. Find the series radius of convergence.
n=1∑∞(x - 6)n/(5n)!
2. Find the interval of convergence of the series.
n=0∑∞(x - 4)2n/16n
3. For what values of x does the series converge absolutely?
n=1∑∞((-1)n+1 (x + 4)n/n10n)
4. For what values of x does the series converge conditionally?
n=1∑∞((-1)n+1 (x + 10)n/n7n)
5. Find the sum of the series as a function of x.
n=0∑∞(x2 + 8/6)n
6. Find the Taylor polynomial of order 3 generated by f at a.
f(x) = 1/7 - x , a = 1
7. Find the Maclaurin series for the given function.
cos 5x
8. Find the Taylor series generated by f at x = a.
f(x) = x4 - 5x2 + 10x + 3, a = -4