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Determine if the series converges or diverges; if the series converges, find its sum. sum_{n=0}^{infty}left(1+frac{3}{n} ight)^{3 n} 

          Determine if the series converges or diverges; if the series converges, find its sum.

sum_{n=0}^{infty}left(1+frac{3}{n}
ight)^{3 n}
Determine if the series converges or diverges; if the series converges, find its sum. sumn=0^inftyleft(1+frac3n ight)^3 n

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Applied Calculus for the Managerial, Life, and Social Sciences
Applied Calculus for the Managerial, Life, and Social Sciences
Soo T. Tan 10th Edition
Chapter 11
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Determine whether the series converges or diverges. If it converges, find its sum. $$\sum_{n=0}^{\infty} \frac{3+2^{n}}{3^{n}}$$

Applied Calculus for the Managerial, Life, and Social Sciences

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Transcript

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00:01 In this question, we are asked to determine whether the given series converges or diverges, and we will start with the divergence test.
00:15 By the divergence test, we need to calculate the limit of the general term of the series, this is the general term of the series, as n goes to infinity, and if this limit is not zero, the series diverges.
00:35 We can rewrite that as the limit of 1 plus 3 over n, cube to the nth power, sorry, 3 over n, 1 plus 3 over n to the nth, and cube, and as n goes to infinity...
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