Multiple Choice

**slevvio** · April 24th 2009, 08:37 AM

Let $\{a_n\}$ be a sequence of positive terms. Which of the following statements is a deduction from :

the sequence $\{a_n\}$ is not summable:

(A) $\forall M > 0 \exists N \in \mathbb{N}$ such that $a_N > M$ .
(B) $a_n \not\rightarrow 0$
(C) $\forall n \in \mathbb{N} \frac{a_{n+1}}{a_n} \le 1$ .
(D) $\forall M>0 \exists N \in \mathbb{N}$ such that $\sum_{i=1}^{N} a_i > M$ .
(E) None of the above.

any help would be apprecaiated - i dont think it can be B or C

**Plato** · April 24th 2009, 09:11 AM

Does the sequence $\left\{ {1,\frac{1}{2},\frac{1}{3}, \cdots ,\frac{1}{n}, \cdots } \right\}$ meet the conditions of this question?

**slevvio** · April 27th 2009, 03:38 AM

Is the answer D) ?

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