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If sum(k = 1)^(oo) (1)/((k + 2)sqrt(k) +...

If `sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c))`, where `a, b, c in N` and `a,b,c in [1, 15]`, then a + b + c is equal to

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