(2/5) + (2/5 * 6/8) * (2/5 * 6/8 * 10/11) * (2/5 * 6/8 * 10/11 * 14/14)....
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Note that
(2/5) + (2/5 * 6/8) + (2/5 * 6/8 * 10/11) + (2/5 * 6/8 * 10/11 * 14/14) + ...
= (2/5) + [(2/5) * (2+4)/(5+3)] + [(2/5) * (2+4)/(5+3) * (2+2*4)/(5+2*3)] + ...
So, we can write this in summation notation as
Σ(n = 0 to ∞) (2 * 5 * ... * (2 + 4n))/(5 * 8 * ... * (5 + 3n)).
I hope this helps!
(2/5) + (2/5 * 6/8) + (2/5 * 6/8 * 10/11) + (2/5 * 6/8 * 10/11 * 14/14) + ...
= (2/5) + [(2/5) * (2+4)/(5+3)] + [(2/5) * (2+4)/(5+3) * (2+2*4)/(5+2*3)] + ...
So, we can write this in summation notation as
Σ(n = 0 to ∞) (2 * 5 * ... * (2 + 4n))/(5 * 8 * ... * (5 + 3n)).
I hope this helps!