
Multiple Choice
Let $\displaystyle \{a_n\}$ be a sequence of positive terms. Which of the following statements is a deduction from :
the sequence $\displaystyle \{a_n\}$ is not summable:
(A) $\displaystyle \forall M > 0 \exists N \in \mathbb{N}$ such that $\displaystyle a_N > M $.
(B) $\displaystyle a_n \not\rightarrow 0 $
(C)$\displaystyle \forall n \in \mathbb{N} \frac{a_{n+1}}{a_n} \le 1$.
(D)$\displaystyle \forall M>0 \exists N \in \mathbb{N} $ such that $\displaystyle \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

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