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Home Infinite Series Properties of Infinite Series Corollaries: Convergent and Divergent Sums | |
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Corollaries: Convergent and Divergent Sums
COROLLARY 1 If converges, then the tails approach zero as m approaches x, PROOF If H is infinite, then so COROLLARY 2 If a series converges, then it remains convergent if finitely many terms are added, deleted, or changed. PROOF If am is the last term changed, then the tail is left unchanged, so it still converges. Warning: Although the convergence properties of a series are not affected by changing finitely many terms, the value of the sum, if finite, is affected.
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Home Infinite Series Properties of Infinite Series Corollaries: Convergent and Divergent Sums |