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answerhappygod
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1. If a power series n=0∑∞anxn converges at x=4, then it converges absolutely at x=−2. 2. If a power series n=0∑∞anxn converges at x=4, then it converges absolutely at x=4. 3. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then f is continuous on its interval of convergence. 4. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then f is has derivatives of all order on (−R,R) and f′(x)=n=0∑∞dxd(anxn)=n=1∑∞nanxn−1 for all x∈(−R,R).
1. If a power series n=0∑∞anxn converges at x=4, then it converges absolutely at x=−2. 2. If a power series n=0∑∞anxn converges at x=4, then it converges absolutely at x=4. 3. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then f is continuous on its interval of convergence. 4. Suppose that n=0∑∞anxn has radius of convergence R>0. Let f(x)=n=0∑∞anxn. Then f is has derivatives of all order on (−R,R) and f′(x)=n=0∑∞dxd(anxn)=n=1∑∞nanxn−1 for all x∈(−R,R).
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