Radius of Convergence

1
Radius of Convergence
Let be a power
series. The set of x for which S(x) converges is
an interval centered at x0 endpoints may or may
not be contained in the interval. The radius of
convergence may be zero, finite, or infinite.
2
Differentiation Integration of Power Series
Let be a power series
with radius of convergence r. The derivative of
S(x) isThe antiderivative of S(x) isBoth A
and D have radius of convergence r.