To infinity and below

Algebra Level 3

\[ \large \sum_{k=2}^\infty \left [\exp_2 \left(-2 + \left(\sum_{i=1}^\infty \dfrac1{k^i} \right)^{-1} \right) \right]^{-1} = \, ? \]

Notation: \(\exp_A (B) \) denotes the exponential function \(A^B\).

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