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## Main Question or Discussion Point

i have to prove that the sum of the follwing infinite series is irrational.

[tex]\frac{1}{2^3} + \frac{1}{2^9} + \frac{1}{2^{27}} + \frac{1}{2^{81}} + \cdots[/tex]

i have no idea where to begin. thanks in advance.

note: this is not a homewrok problem.

[tex]\frac{1}{2^3} + \frac{1}{2^9} + \frac{1}{2^{27}} + \frac{1}{2^{81}} + \cdots[/tex]

i have no idea where to begin. thanks in advance.

note: this is not a homewrok problem.