Sum!

I think I got it is it $\frac{2^1}{14175}$, but how would you express $b?$

I get    2^9 / 10!       (a,b) = (9,10)

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Note that  we can write

10!  [ 1 / (9! * 1! )  + 1 / (3!*7! )  + 1/ (5!*5!) + 1/ (7!*3!) + 1/(9!*1!) ]  =

10! / (9! * 1!) + 10! / (3!*7!) + 10! / (5!*5!) + 10! / (7!*3!) + 10!/(9!*1!)  

C(10, 1)  + C(10, 3) + C(10, 5)  + C(10,3) + C(10,1)  =

2 C(10, 1)  + 2 (10, 3) + C(10, 5)   =

20  + 240   +  252  =

512

So

10!  [ 1 / (9! * 1! )  + 1 / (3!*7!  + 1/ (5!*5!) + 1/ (7!*3!) + 1/(9!*1!) ]  =  512

[ 1 / (9! * 1! )  + 1 / (3!*7!  + 1/ (5!*5!) + 1/ (7!*3!) + 1/(9!*1!) ]  =  512 / 10!  =  2⁹ / 10!

(a , b)  =  (9, 10)

Thank you, guys!