Let x; be a series of complex numbers. (i) Suppose that there exist No E N,...
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Let Σx; be a series of complex numbers. (i) Suppose that there exist No E N, k> 0 and a convergent series of real numbers #fm1 y, such that y, ≥ 0 and |xn| <ky, for all n > No. Prove that x, is (absolutely) convergent; (II) Suppose that there exists 0 <c<1 and No EN such that √x Se for n No. Prove that Σx, is (absolutely) convergent. (iii) Suppose that there exists 0 < c < 1 and No EN such that Ixal (absolutely) convergent. 100 <e for n > No. Prove that X, is Let Σx; be a series of complex numbers. (i) Suppose that there exist No E N, k> 0 and a convergent series of real numbers #fm1 y, such that y, ≥ 0 and |xn| <ky, for all n > No. Prove that x, is (absolutely) convergent; (II) Suppose that there exists 0 <c<1 and No EN such that √x Se for n No. Prove that Σx, is (absolutely) convergent. (iii) Suppose that there exists 0 < c < 1 and No EN such that Ixal (absolutely) convergent. 100 <e for n > No. Prove that X, is
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Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
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