Does there exist a formula for the sum of n^m numbers?

AI Thread Summary
The discussion centers on the existence of a general formula for the sum of the first n^m numbers, where m is an integer. While formulas are known for sums of the first n natural numbers, squares, and cubes, the conversation seeks to explore whether similar formulas exist for higher powers. Participants reference Faulhaber's formula as a potential solution for calculating these sums. The inquiry emphasizes the need for a comprehensive approach to sums involving higher integer powers. Overall, the quest for a generalized formula for n^m sums remains a topic of interest in mathematical exploration.
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is there a general formula for the sum of the first

n^m numbers where m is an integer

i know there exists one for the 1+2+...+n and the sum of squares and the sum of cubes

but what about higher powers? And what about a general formula
 
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