Question
What are all values of x for which the series \(\sum_{n=1}^{\infty }\frac{(x-2)^n}{n.3^{n}}\) converges?
(A) −3≤x ≤ 3
(B) −3< x< 3
(C) −1< x ≤ 5
(D) −1≤x ≤ 5
(E) −1≤x < 5
Answer/Explanation
Ans:E
Question
The interval of convergence of\sum_{n=0}^{\infty }\frac{(x-1)^{n}}{3^{n}} is
(A)\(-3<x\leq 3\) (B)\(-3\leq x\leq 3\) (C)\(-2<x<4\) (D)\(-2\leq x<4\) (E)\(0\leq x\leq 2\)
Answer/Explanation
Ans:C
Question
If \(S_{n}=\left ( \frac{(5+n)^{100}}{5^{n+1}} \right )\left ( \frac{5^{n}}{(4+n)^{100}} \right ){s_{n}}\)
(A)\(\frac{1}{5}\) (B)1 (C)\(\frac{5}{4}\) (D)\(\left ( \frac{5}{4}\right )^{100}\) (E) The sequence does not converge.
Answer/Explanation
Ans:A
Question
For what integer k, k >1, will both \(\sum_{n=1}^{\infty }\frac{(-1)^{kn}}{n} \) and \(\sum_{n=1}^{\infty }\left ( \frac{k}{4} \right )^{n}\) converge?
(A) 6 (B) 5 (C) 4 (D) 3 (E) 2
Answer/Explanation
Ans:D
The first series is either the harmonic series or the alternating harmonic series depending on