Question Number 66910 by naka3546 last updated on 20/Aug/19
$${P}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}\right)} \\ $$$${Q}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{999}+{n}\right)\left(\mathrm{1999}−{n}\right)} \\ $$$$\frac{{P}}{{Q}}\:\:=\:\:? \\ $$
Commented by naka3546 last updated on 20/Aug/19
$${Is}\:\:{it}\:\:{correct}\:\:{if}\:\:{the}\:\:{answer}\:\:\mathrm{1499}\:? \\ $$