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February 20th, 2019, 10:20 AM   #11
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I gave the values ​​of the suite until n.(u0 u1 ....un)
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February 20th, 2019, 01:59 PM   #12
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That wasn't done in your opening post and you should have started with U1 and U2 instead of U0 and U1. As it stands, you never defined U2.

I had already obtained (n² + n - 84)/2, and your formula can be obtained from that by replacing n with n+7 and gathering like terms. With the above renumbering, your formula will give the sum correctly if there is more than one term. Producing a single formula that also works for just one term requires allowing an ugly formula that's awkward to work with.

If there's more than one term, the formula n = $\lfloor$√(2Sn + 84)$\rfloor$ - 7 gives n in terms of Sn.
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