Cho F=(-9/25).53/3-(-3/5)^2.22/3 và . Khi đó tổng F + P bằng

* Hướng dẫn giải

Đáp án cần chọn là: C

$\begin{array}{l}F=\left(-\frac{9}{25}\right).\frac{53}{3}-{\left(-\frac{3}{5}\right)}^2.\frac{22}{3}\\ =-\frac{9}{25}.\frac{53}{3}-\frac{9}{25}.\frac{22}{3}\\ =-\frac{9}{25}.\left(25\right)\\ =-9\end{array}$

$\begin{array}{l}\begin{array}{l}P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)\mathrm{...}\\ \mathrm{...}\left(1-\frac{1}{999}\right).\left(1-\frac{1}{1000}\right)\end{array}\\ =\frac{1}{2}.\frac{2}{3}.\frac{3}{4}\mathrm{.....}\frac{998}{999}.\frac{999}{1000}\\ =\frac{\mathrm{1.2.3.....999}}{\mathrm{2.3.4...999.1000}}=\frac{1}{1000}\end{array}$

$F+P=\frac{1}{1000}+(-9)=-\frac{8999}{1000}$