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gulaghasi [49]
2 years ago
5

Please answer as soon as possible! Brainliest and lots of points! Please give good details and make sense! Thanks! (See attachme

nt for question)

Mathematics
1 answer:
professor190 [17]2 years ago
6 0

Answer:

no because they did not multiply the whole numbers and just multiplied the powers

Step-by-step explanation:

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Consider the following series. 1 9 1 18 1 27 1 36 1 45 Determine whether the series is convergent or divergent. Justify your ans
Vedmedyk [2.9K]

Answer:

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

Step-by-step explanation:

<u>Convergence of Infinite Series</u>

The series is given as the terms

1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...

For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.

Our series has two clearly different sequences, which define it as a piecewise general term:

If n is odd, then

a_n=1

Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is

a_n=9+9(n/2-1)=4.5n

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If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.

The limit of the function

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But it goes worse because of the limit of the second piece

a_n=4.5n

when n goes to infinity is infinite.

The answer is

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

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Step-by-step explanation:

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