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December 25th, 2016, 03:39 PM   #1
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Summation of powers of powers

I have recently been asked to create a formula for the summation between 1 and N for 2^A^X where A is a given number and X is the variable. After attempting to approach this via various methods, I found that it end up simplifying to 2^A (1 + 2^A (1 + 2^AxA (1 + 2^AxAxA ... which suggests that without knowing A, there is no definitive formula for this series. Can anyone give an answer as to why this is the case or an alternative method for getting a solution that improves on the above one.
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December 25th, 2016, 04:44 PM   #2
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Summation between 1 and N or 1 and X?

$\sum_{1}^{N}$ 2^A^X = N(2^A^X)$ or am i being daft

Last edited by Joppy; December 25th, 2016 at 04:52 PM.
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December 26th, 2016, 05:46 AM   #3
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integer values between one and n are subbed into X and added together
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