论文标题
一个简单的助记符计算权力总和
A simple mnemonic to compute sums of powers
论文作者
论文摘要
我们给出一个简单的递归公式，以获取$ r $ th功率的第一个$ n $自然数的一般总和。我们的方法允许人们获得$（r+1）$ th功率的通用公式，一旦知道$ r $ th功率的通用公式。由于与分化和集成的类比，该方法非常容易记住。与以前已知的方法不同，不需要其他特定常数（例如Bernoulli数字）。这使得在无法咨询外部参考（例如数学竞赛）的情况下特别适合应用程序。
We give a simple recursive formula to obtain the general sum of the first $N$ natural numbers to the $r$th power. Our method allows one to obtain the general formula for the $(r+1)$th power once one knows the general formula for the $r$th power. The method is very simple to remember owing to an analogy with differentiation and integration. Unlike previously known methods, no knowledge of additional specific constants (such as the Bernoulli numbers) is needed. This makes it particularly suitable for applications in cases when one cannot consult external references, for example mathematics competitions.
