shamieh
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Determine if the positive term series is convergent or divergent
$$
\sum^{\infty}_{n = 0} \frac{(2n + 3)^2}{(n + 1)^3}$$
So what I did was look at it as 2n + 3/n + 1 , then I did the limit as n --> infinity using lopitals to get 2/1 which = 2. Then i said this must be divergent since lim a_n as n -> infty is != to 0 by the nth term test this diverges. Would that be correct?
$$
\sum^{\infty}_{n = 0} \frac{(2n + 3)^2}{(n + 1)^3}$$
So what I did was look at it as 2n + 3/n + 1 , then I did the limit as n --> infinity using lopitals to get 2/1 which = 2. Then i said this must be divergent since lim a_n as n -> infty is != to 0 by the nth term test this diverges. Would that be correct?