## Calculus, 10th Edition (Anton)

Given $$\left\{ n- n^2\right\}_{1}^{\infty}$$ Since $a_n=n- n^2,\ \ a_{n+1}= n+1- (n+1)^2$, then \begin{align*} a_{n+1}-a_n&= n+1- (n+1)^2-n+n^2\\ &= n+1-n^2-2n-1-n+n^2\\ &= -2n\leq0 \end{align*} So, the sequence is strictly decreasing