Doing Sums

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Doing Sums
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What is ?
Let a 1 and r 1/2
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What if k starts at 1?
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So we have two more closed form solutions
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Solve
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Find
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Find
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Derive the closed form for
First we note that k3 - (k-1)3 3k2-3k1, then
we sum both sides of the equation from 1 to n
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Rearranging the terms, we get
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