Question

Determine all of the values of x for which the following series converges. Choose the best answer.\\ $\sum_{n=1}^{\infty} \frac{x^n}{n^3}$\\Hint: remember to check each endpoint!\\$-1 < x < 1$\ $-1 \le x < 1$\ $-1 < x \le 1$\ $-1 \le x \le 1$\ Question 6\\Find the test value $L = \lim_{n \to \infty} |\frac{a_{n+1}}{a_n}|$ that you could use to apply the ratio test to the following series:\ $\sum_{n=1}^{\infty} \frac{n+1}{n!}$\\$L = \infty$\ $L = \frac{1}{2}$\ $L = 0$\ $L = 1$\ The limit to compute $L$ does not exist

          Determine all of the values of x for which the following series converges. Choose the best answer.\\
$\sum_{n=1}^{\infty} \frac{x^n}{n^3}$\\Hint: remember to check each endpoint!\\$-1 < x < 1$\
$-1 \le x < 1$\
$-1 < x \le 1$\
$-1 \le x \le 1$\
Question 6\\Find the test value $L = \lim_{n \to \infty} |\frac{a_{n+1}}{a_n}|$ that you could use to apply the ratio test to the following series:\
$\sum_{n=1}^{\infty} \frac{n+1}{n!}$\\$L = \infty$\
$L = \frac{1}{2}$\
$L = 0$\
$L = 1$\
The limit to compute $L$ does not exist

Determine all of the values of x for which the following series converges. Choose the best answer.

∑n=1^∞(x^n)/(n^3)
Hint: remember to check each endpoint!
-1 < x < 1-1 ≤ x < 1-1 < x ≤ 1-1 ≤ x ≤ 1Question 6
Find the test value L = limn →∞ |(an+1)/(an)| that you could use to apply the ratio test to the following series:∑n=1^∞(n+1)/(n!)
L = ∞L = (1)/(2)L = 0L = 1The limit to compute L does not exist

Added by Edward B.

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