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I want to check convergence for the following series:

∑2^(1/n)-1

so that's the n'th root of two minus one, for n going to positive infinity

Now all possible formulas i know come out inconclusive,

so the only formula i can think of is the integer formula, now i thought

to make things easier to just integrate 2^(1/n) and if this series proves to be convergent then that proves the convergency (as it is always "1" larger than the other one).

Now as i am seem to be a complete idiot i cannot even find the integer for this one.

Can someone help me?

Sorry if my English is not so good.

Thank you in advance,

Egwin.