MAT 137Y: Calculus with proofs
Due on Thursday, March 25 by 11:59pm via Crowdmark
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• You will need to submit your answer to each question separately.
• This problem set is about Unit 13.
1. (a) Prove the following Theorem
Theorem 1. Let
an be a series.
an = 0
THEN the series
an is convergent.
Hint: You may use results from past assignments. They will make things simpler.
(b) Prove that the theorem is false if we remove any one of the two hypotheses.
an be a CONVERGENT, NON-NEGATIVE series. Let f is a continuous function
with domain R. Decide whether each of the following series must be convergent, must be
divergent, or we do not have enough information to decide. Prove it.
(nn · an)
ln (2 + an)
2 + an+1
2 + an
ln (1 + an)
(an f(sinn)) 学霸联盟