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Math Help - prove that 1/(2^(2n)) converges

  1. #1
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    prove that 1/(2^(2n)) converges

    PLease help i've totally forgotten how to do this i know it has something to do with the sequences of partial sums.

    Show that (the sum from n=1-infinity) of 1/(2^(2n)) converges.

    Sorry bout the crap way of writing it.
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  2. #2
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    comparison test with 1 / 2^n
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  3. #3
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    Hello,

    Just use basic rules of exponents :
    (a^b)^c=a^{bc}

    Hence 2^{2n}=(2^2)^n=4^n

    Is  \sum_{n=1}^\infty \frac{1}{4^n} a convergent series ?

    Hint : think geometric
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