A Note on the Alternating Sums of Powers of Consecutive Integers
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چکیده
For n, k ∈ Z≥0, let Tn(k) be the alternating sums of the n-th powers of positive integers up to k − 1: Tn(k) = ∑ k−1 l=0 (−1)l. Following an idea due to Euler, we give the below formula for Tn(k): Tn(k) = (−1) 2 n−1 ∑ l=0 (n l ) Elk n−l + En 2 (
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تاریخ انتشار 2005