Determine whether the following statements are true and give an explanation or counterexample. a. If converges, then

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Determine whether the following statements are true and give an explanation or counterexample.

a. IfΣο Οκ k=1 converges, thenак k=10 Σ converges.
b. If diverges, then diverges.

c. If ∑ak converges, then ∑(ak + 0.0001) also converges.

d. If ∑pk diverges, then ∑(p + 0.001)k diverges, for a fixed real number p.

e. If ∑k-p converges, then ∑k-p + 0.001 converges.

f. Ifthen ∑ak converges.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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