Series - math.ucdavis.edu
A condition for the convergence of series with positive terms follows immedi-ately from the condition for the convergence of monotone sequences. Proposition 4.6. A series P a nwith positive terms a n 0 converges if and only if its partial sums Xn k=1 a k M are bounded from above, otherwise it diverges to 1. Proof. The partial sums S n= P n k=1 a
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