Answer Happy

T/F?
1. The radius of convergence of a power series is either 0,1 or ∞. If f(x)=n=0∑∞​an​xn for all x, then f′(x)=n=1∑∞​nan​xn−1 for all x. 3. If f(x)=n=0∑∞​an​xn for all x, then ∫f(x)dx=C+n=0∑∞​an​n+1xn+1​ for all x. 4. If R>0 and f(x)=n=0∑∞​an​xn for all x∈(−R,R), then an​=n!f(n)(0)​ for all n.