Saved Bookmarks
| 1. |
Let \(\left<x_n\right>\) and \(\left<y_n\right>\) be real sequences and let for some k ϵ N, 0 ≤ xn ≤ yn for n ≥ k.Then, which of the following statements is true?1. Divergence of ∑ yn ⇒ Divergence of ∑ xn2. ∑ xn and ∑ yn are always divergent3. Convergence of ∑ xn ⇒ Convergence of ∑ yn4. Convergence of ∑ yn ⇒ Convergence of ∑ xn |
|
Answer» Correct Answer - Option 4 : Convergence of ∑ yn ⇒ Convergence of ∑ xn Concept: The convergence or divergence of sequences is tested by various methods. One is Comparison test. Comparison test: Suppose that we have two series ∑an and ∑bn with an, bn ≥ 0 for all n and an ≤ bn for all n. Then, 1. If ∑bn is convergent then so is ∑an 2. If ∑an is divergent then so is ∑bn The statement 1 is given in the 4th option. |
|