An algebra problem by Ankit Nigam
Algebra
Level
5
Find the value of positive integer \(n\) for which the quadratic equation \[\displaystyle \sum_{k = 1}^n(x + k - 1)(x + k) = 10n\]
has solutions \(\alpha\) and \(\alpha + 1\) for some value of \(\alpha\).
by
Ankit Nigam