How to generalize the terms of this series?

Given the series {a_n} = 1/(2^n) + 1/(3^n), generalize the terms of the series for a_2k and a_2k-1. Thanks for any help.

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  • 1 decade ago
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    {a_n} = 1/(2^n) + 1/(3^n)

    When n = 2k

    {a_2k} = 1/(2^(2k)) + 1/(3^(2k)) = 1/(4^k) + 1/(9^k), k= 1,2, ...

    When n = 2k-1

    {a_2k-1} = 1/(2^(2k-1)) + 1/(3^(2k-1)) = 2/(4^k) + 3/(9^k), k= 1,2, ...

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