Recent questions tagged sequences

Let $p(x)$ be a polynomial in $x$ of degree $k \geq 0$. For $n=1,2, \ldots$, define $a_{n}=p(n+1)-p(n)$. If $\left\{a_{n}\right\}_{n=1}^{\infty}$ is in AP, then we must h...

Consider two real-valued sequences $\left \{ x_{n} \right \}$ and $\left \{ y_{n} \right \}$ satisfying the condition $x^{3}_{n} - y^{3}_{n} \rightarrow 0$ as $n \righta...