When f(x) is represented by the power series ∑n=0∞cn(x−3)n with radius of convergence R, a student integrates the series term-by-term to obtain g(x)=∑n=0∞n+1cn(x−3)n+1+C. Which statement about the convergence of the series for g(x) is correct?
a) The radius of convergence of the series for g is R+1.
b) The series for g converges for every real x (that is, its radius of convergence is infinite).
c) The radius of convergence of the series for g equals R.
d) The radius of convergence of the series for g is R−1.