# Taylor series of digamma

Calculus Level 5

$\large \sum_{n=2}^\infty \zeta(n)z^n=-\int_0^1 az\dfrac{x^{-z+b}-c}{x^{b+1}-c} \, dx$

The equation above holds true for $$|z| < 1$$ and integer constants $$a,b$$ and $$c$$.

Find the value of $$a+b+c$$.

Notation: $$\zeta(\cdot)$$ denotes the Riemann zeta function.

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