Is there a general method to find the sum of powers with negative exponent?
For example: $\sum_{i = 1}^{N} i^a$ with $ a \in \mathbb{Z} - \mathbb{N}$
2025-01-13 07:59:02.1736755142
Is there a general method to find $\sum_{i = 1}^{N} i^a$
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This is the definition of the generalized harmonic numbers. Assuming $a>0$ $$\sum_{i=1}^n\frac 1 {i^a}=H_n^{(a)}$$