Answer by Adam Rubinson for Has it been proven that, if $\ y_n = x_{n+1} -...
Now I realise my question is a bit silly and the answer is trivially "no". I'm not sure what I was trying to get at with the question, but I must have been thinking unclearly at the time and muddling...
View ArticleAnswer by caduk for Has it been proven that, if $\ y_n = x_{n+1} - x_n\ $ is...
If $y_n$ is increasing, $y_n\geq n+y_0$ for all $n$, so $x_n\geq \frac{n(n-1)}{2}+ny_0 + x_0$.$x_n$ is of quadratic growth, so the sum of reciprocals converges, thus it can't be a counter-example.If...
View ArticleHas it been proven that, if $\ y_n = x_{n+1} - x_n\ $ is non-decreasing, then...
I'm trying to find a subset $\ A\ $ of $\ \mathbb{N}\ $ that disproves Erdős Conjecture on Arithmetic progressions.If we instead write $\ A\ $ as a (strictly) increasing sequence of integers, $\...
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