Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 828: 72

$-300$

Recall the formulas: $A) \displaystyle \sum_{k=1}^{n} k =\dfrac{n(n+1)}{2} \\ B) \displaystyle \sum_{k=1}^{n} (-k)=- \sum_{k=1}^{n} (k) $ Use formula $(B)$ to obtain: $\displaystyle \sum_{k=1}^{24} (-k) =- \sum_{k=1}^{24} (k)$ Use formula $(A)$ to obtain: $ - \displaystyle \sum_{k=1}^{24} k= -[ \dfrac{24(24+1)}{2}] \\= -300$