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wellfed · #5 July 3rd, 2009, 05:16 PM

Quote:

Originally Posted by Jose27

Suppose $0 \leq a_1 \leq ...\leq a_n \leq ...$ and that $\lim_{n \rightarrow \infty} na_n$ $=L$ then $\sum_{i=1}^n {a_i}$ $\leq na_n \leq L$ for all $n \in \mathbb{N}$ and so the series converges.

but then a_n=0 for all n \in \mathbb{N} so it doesn't work. I'll check it later.

your assumption $0 \leq a_1 \leq ...\leq a_n \leq ...$ and that $\lim_{n \rightarrow \infty} na_n$ $=L$ are not compatible.