$\text { Determine if the series } \sum _ { n = 1 } ^ { \infty } a _ { n } \text { defined by the formula converges or diverges. }$
-$$a _ { 1 } = 7 , a _ { n + 1 } = \frac { 3 n - 7 } { 4 n - 5 } a _ { n }$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

We can use ratio test to check the convergence of the given series. Using ratio test, we have:
\begin{align*}
\lim_{n	o\infty} \left| \frac{a_{n+1}}{a_n} ight| &= \lim_{n	o\infty} \left| \frac{(3n-7)a_n}{(4n-5)a_n} ight| \
&= \lim_{n	o\infty} \left| \frac{3n-7}{4n-5} ight| \
&= \frac{3}{4}.
\end{align*}
Since the limit is less than 1, by ratio test, the series converges. Therefore, the correct choice is A) Converges.

Determine if the series ∑n=1∞an defined by the formula converges or diverges. \text { Determine if the series } \sum _ { n = 1 } ^ { \infty } a _ { n } \text { defined by the formula converges or diverges. } Determine if the series ∑n=1∞​an​ defined by the formula converges or diverges.

$\text { Determine if the series } \sum _ { n = 1 } ^ { \infty } a _ { n } \text { defined by the formula converges or diverges. }$