Number Theory Level pending

For all $$n\ge 2$$, there are $${ p }_{ n }$$ the prime number less than or equal to $$n$$ and $${ q }_{ n }$$ the next prime number larger than $$n$$. For example: $$n=3$$, $${ p }_{ 3 }=3$$ and $${ q }_{ 3 }=5$$.

Find the value of

$\frac { 1 }{ { p }_{ 2 }{ q }_{ 2 } } +\frac { 1 }{ { p }_{ 3 }{ q }_{ 3 } } +\frac { 1 }{ { p }_{ 4 }{ q }_{ 4 } } +\frac { 1 }{ { p }_{ 5 }{ q }_{ 5 } } +\frac { 1 }{ { p }_{ 6 }{ q }_{ 6 } } +\frac { 1 }{ { p }_{ 7 }{ q }_{ 7 } } +\frac { 1 }{ { p }_{ 8 }{ q }_{ 8 } } +\frac { 1 }{ { p }_{ 9 }{ q }_{ 9 } } +\frac { 1 }{ { p }_{ 10 }{ q }_{ 10 } }$

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