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Expert: - 5/21/2008


Question
Hi Paul,
How do I find the sum of the series
2+sqrt(2)+cuberoot(2)+fourthroot(2)+... if it exists.

Thanks!


Answer
Questioner:   vince
Category:  Advanced Math
Private:  No
 
Subject:  series
Question:  Hi Paul,
How do I find the sum of the series
2+sqrt(2)+cuberoot(2)+fourthroot(2)+... if it exists.

Thanks!
....................................
Hi, Vince

... if it exists.

THAT'S THE CLUE!  You have to be sure it exists first.

An absolute requirement is that the individual terms converge to zero.

But  lim [n->inf] 2^(1/n) = 1, not zero.  So this series diverges.

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