February 20th, 2019, 10:20 AM  #11 
Banned Camp Joined: Feb 2019 From: France Posts: 8 Thanks: 0 
I gave the values of the suite until n.(u0 u1 ....un)

February 20th, 2019, 01:59 PM  #12 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
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. 