Question 610037
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Hi, 
The sum of the reciprocals of two consecutive positive odd integers is 16/63
{{{1/(n) + 1/(n+2) = 16/63}}}
  63(n+2) + 63n = 16n(n+2)              |||Multiplying thru by 63n(n+2) so as all denominators = 1
  16n^2 - 94n - 126 = 0
{{{x = (94 +- sqrt(16900 ))/(32) }}}
  n = 7, tossing out negative solution
   7 and 9 are the two consecutive positive odd integers
CHECKING our Answer***
1/7 + 1/9 = 16/63