Question

8. Does the series converge absolutely, converge, or diverge? Give a reason for your answer.\ $frac{1}{6} - frac{1}{9} + frac{1}{12} - frac{1}{15} + frac{1}{18} - frac{1}{21} + dots$\ Choose the correct answer below.\ A. The series diverges because the nth term does not approach zero.\ B. The series converges absolutely because $sum frac{1}{3(n+1)}$ converges by limit comparison with $sum frac{1}{n}$. C. The series converges conditionally; $sum (-1)^{n+1} frac{1}{3(n+1)}$ converges by the alternating series test; $sum frac{1}{3(n+1)}$ diverges by limit comparison with $sum frac{1}{n}$. D. The series diverges; $sum frac{1}{3(n+1)}$ diverges by limit comparison with $sum frac{1}{n}$.

          8. Does the series converge absolutely, converge, or diverge? Give a reason for your answer.\
$frac{1}{6} - frac{1}{9} + frac{1}{12} - frac{1}{15} + frac{1}{18} - frac{1}{21} + dots$\
Choose the correct answer below.\
A. The series diverges because the nth term does not approach zero.\
B. The series converges absolutely because $sum frac{1}{3(n+1)}$ converges by limit comparison with $sum frac{1}{n}$.
C. The series converges conditionally; $sum (-1)^{n+1} frac{1}{3(n+1)}$ converges by the alternating series test; $sum frac{1}{3(n+1)}$ diverges by limit comparison with $sum frac{1}{n}$.
D. The series diverges; $sum frac{1}{3(n+1)}$ diverges by limit comparison with $sum frac{1}{n}$.

$8. Does the series converge absolutely, converge, or diverge? Give a reason for your answer.frac16 - frac19 + frac112 - frac115 + frac118 - frac121 + dotsChoose the correct answer below.A. The series diverges because the nth term does not approach zero.B. The series converges absolutely because sum frac13(n+1) converges by limit comparison with sum frac1n. C. The series converges conditionally; sum (-1)^n+1 frac13(n+1) converges by the alternating series test; sum frac13(n+1) diverges by limit comparison with sum frac1n. D. The series diverges; sum frac13(n+1) diverges by limit comparison with sum frac1n.$

Added by Christopher G.

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