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If lim(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(...

If `lim_(n->oo)(1(2n-1)^(k)+2(2n-2)^(k)+3(2n-3)^(k)+...+n.n^(k))/(n^(k+1))=(2^(k+a)-2)/(k+1)+(1-2^(k+b))/(k+2)`where `a, b, k in N` and `k >= 5` then the value of `(a+b)/(3)` is

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