Use the Ratio Test to determine the convergence or divergence of the series .
A)converges
B)diverges

Name: Use the Ratio Test to determine the convergence or divergence of the series . A)converges B)diverges
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Question

Use the Ratio Test to determine the convergence or divergence of the series  . ​
A)converges 
B)diverges

Quizplus · Accepted Answer

Applying the Ratio Test, we have:

|(a_{n+1})/(a_n)| = |(11*(n+1)/((n+1)^2 + 2)) / (11*n/(n^2 + 2))|

= |(11*(n+1)*(n^2+2))/(11*n*(n^2+2) + 2(n+1)))|

= |(11n^3 + 22n)/(11n^3 + 2n + 2)|

As n approaches infinity, the ratio reduces to 11, which is greater than 1. Hence, the series diverges.

Use the Ratio Test to Determine the Convergence or Divergence