Question
What are all values of x for which the series \(\sum_{n=1}^{\infty }\frac{(x-)^{n}}{n}\) converges?
(A) −1≤ x< 1 (B) −1 ≤ x≤ 1 (C) 0< 2 < x (D) 0 ≤ x <2 (E) 0 ≤ x ≤ 2x
Answer/Explanation
Ans:D
The center is x = 1, so only C, D, or E are possible. Check the endpoints.
At\(x=o:\sum_{n=1}^{\infty }\frac{(-1)^n}{n} \) converges by alternating series test.
Question
If the nth partial sum of a series \(\sum_{i=1}^{\infty }a_{i}\) is \(s_{n}=\frac{3n+1}{2n-5}\) find \(a_{5}\).
(A) \(\frac{3}{2}\)
(B) \(\frac{17}{5}\)
(C) \(-\frac{17}{15}\)
(D) \(\frac{16}{5}\)
Answer/Explanation
Ans:(C)