ExAM 2 RETAKE (11.1-11.7) P 1 . Suppose {6.)?. is a sequence, and {*»)T-, is its

Question

ExAM 2 RETAKE (11.1-11.7) P 1 . Suppose {6.)?. is a sequence, and {*»)T-, is its wynence of partial sum" A. Suppose the sequence (o. couverges to 4. Circle ALL correct statemets, and explaim a. The b. The seriesdiverges c. We do not have enough information to determine if "?-eonvergm or diners B. Suppose the sequence (o).converges to o. Circke ALL correct statewents, and explain a. The seriesCORVErges b. The seriesdiverges c. We do not have enough information to determine if Cs or diverges C. Suppose the seriscomverges to 4. Circle ALL correct statements, and esplain a. The sequence {a.) oonverges. We do not have enough information to find the limit. b. The sequence (a diverges c. We do not have enough information to determine it fa)i couverges or diverges d. The sequence {a"} converges to 0.

Explanation / Answer

1A

It is stated that the given sequence converges to 4.This means that the terms of the sequence ' tend to a limit' that exists. In this case it is Limn->inf an =4. Rule book says, 'A sequence whose nth term an is not =0, diverges'. In view of this,

(a) Statement is not correct

(b)Statement is correct.

(c) Statement is not correct. We do have the information that the series diverges.

(d)Statement is not correct. It is the nth term, which converges to 4. It does not mean that partial sums converge to 4

B If the nth term of a sequence converges to 0, the series can (sum of partial sums) converge or diverge. Limn->inf an =0 is not a sufficient condition for convergence of series. More information would be needed to determine if the series converges.. In view of this,

(a)Statement is not correct. Series may converge or diverge.

(b)Statement is not correct. Series may converge or diverge.

(c)Staement is correct

(d)Statement is not correct. Sequence converges to 0 does not mean partial sums also converges to 0

C.

(a)The statement consists of two parts. First part is correct, the sequence has to be convergent as partial sums of a divergent sequence cannot be convergent. The second part is not correct, because the limit of sequence of terms of a convergent series cannot be other than 0. On the whole , statement is not correct.

(b)The statement is not correct. The sequence of a convergent series has to converge to 0

(c)The statement is not correct. The sequence of terms has to be convergent and must converge to 0

(d) Statement is correct

(e)Statement is correct

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