探究第二类自然数幂和通项公式的方法及其运用

The exploration for the general formulas of sum formulas of the second natural numbers and its application

针对第二类自然数幂和问题,利用二项式定理,得到了一种求解第二类自然数幂和的隐式通项公式,通过MATLAB编程求解隐式公式,并将该通项公式应用于实际问题中,验证公式的有效性和适用性。实例表明,该公式的优点是计算简单,具有普遍性和广泛的运用领域。

For the problem of sum the second natural numbers, an implicit general formulas, which is solved by MATLAB software, is presented by the binomial theorem. The validity and applicability of the implicit general formulas are verified through some samples application. The application results show the implicit general formulas has simple calculation and widely applicable.