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answerhappygod
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1. The series n=0∑∞anxn and n=0∑∞ann+1xn+1 have the same radius of convergence. 2. The series n=0∑∞anxn and n=0∑∞ann+1xn+1 have the same interval of convergence. 3. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then an=n!f(n)(0) for each n∈N∪{0}.
1. The series n=0∑∞anxn and n=0∑∞ann+1xn+1 have the same radius of convergence. 2. The series n=0∑∞anxn and n=0∑∞ann+1xn+1 have the same interval of convergence. 3. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then an=n!f(n)(0) for each n∈N∪{0}.
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