Infinite summation of an infinite summation?

Calculus Level 3

\[\large \displaystyle \sum_{n=2}^{\infty} (\zeta(n) - 1)\]

The Riemann zeta function is defined as \(\zeta(s)=\displaystyle \sum_{r=1}^{\infty} \dfrac{1}{r^s}\). Find the value of the above expression.

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