Let $c > 0$. I am trying to obtain an upper bound for $$ |X^{c}/c - \sum_{1 \leq t \leq X} t^{c-1}|. $$ I am sure this is pretty small as $\int_{1}^X t^{c-1} dt = X^c/c - 1$. What is the best way to treat this when we have a sum instead? Any comments/suggestions are appreciated. Thank you!
2026-03-29 22:31:48.1774823508
How to esimate $X^{c}/c - \sum_{1 \leq t \leq X} t^{c-1}$
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