Prove that if the series converges then the series likewise converges. Also, offer an example to present that the converse is false, i.e., a instance in which converges however does not.
You are watching: If an converges then an^2 converges
Proof. Assume converges. Then we know
The first sum is a finite amount so it converges, and the second sum converges by comparison via . Hence, converges
Counterinstance. The converse is false. Let
Prove that if ∑ an converges then ∑ (an)1/2 n-p converges for p > 1/2
Prove that ∑ 1/an diverges if ∑ an converges
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A really awesome book that I extremely recommend on exactly how to examine math and be a math major is Laura Alcock"s, How to Study as a Mathematics Major:
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Basics: Calculus, Linear Algebra, and Proof WritingCore Mathematics Subjects.
See more: Letra De Los Peces En El Rio, Los Peces En El Rio: Canción Con Letra
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