According to me the answer should be infinity, since the series is increasing and common ratio is greater than 1. But is my reasoning correct?
@Brian Charlesworth

Yes, that's correct. The \(n\)th term is of the form \(a(n) = 2^{n}(2n - 1),\) which goes to \(\infty\) as \(n \rightarrow \infty,\) and so by the \(n\)th term test we conclude that the series diverges.

Just out of curiosity, note that the sum of the first \(N\) terms of this series is \((2N - 3)2^{N+1} + 6.\)

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## Comments

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TopNewestThe series does not converge.

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ok so is the answer infinity. @Nihar Mahajan

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I guess yes.

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According to me the answer should be infinity, since the series is increasing and common ratio is greater than 1. But is my reasoning correct? @Brian Charlesworth

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Yes, that's correct. The \(n\)th term is of the form \(a(n) = 2^{n}(2n - 1),\) which goes to \(\infty\) as \(n \rightarrow \infty,\) and so by the \(n\)th term test we conclude that the series diverges.

Just out of curiosity, note that the sum of the first \(N\) terms of this series is \((2N - 3)2^{N+1} + 6.\)

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Thank You Sir.

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