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I've been told, the following series converges: $$\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\ldots+\frac{1}{2k}+\ldots$$

I can't get my head around, how to prove this converges; any hints?

  • 4
    Did you mean *the sequence* $\{1/2\,,\,/14\,,...\,1/2k\,,...\}\,$ or *the series* $$\frac{1}{2}+\frac{1}{4}+...=\sum_{n=1}^\infty\frac{1}{2n}\,\,?$$2012-09-10
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    I had meant the 'series', sorry for the incorrect wording.2012-09-10
  • 0
    This sequence is clearly divergent!2012-10-05

2 Answers 2