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The series $x + x^{1 + \frac{1}{2}} + x^{1 + \frac{1}{2}+ \frac{1}{3}} +...$ is convergent if

(A) $x>e$

(B) $x

(C) $x<1/e$

(D) $x>1/e$

I think the answer is C, but I could not determine the condition... how to solve it. Plz help.

  • 0
    As the others are obviously wrong (no convergerce for $x = 1$ and $x= 10$) ... (C) ist the answer ...2012-10-09
  • 0
    I think it is difficult to solve analytically, but all other than (C) can be pretty easily ruled out.2012-10-09
  • 0
    What if (D') $1/e? How to exclude it?2012-10-09

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