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P-n-1-999-1-2n-1-2n-Q-n-1-999-1-999-n-1999-n-P-Q-




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

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