Question

If \((20)^{19}\) + \(2(21)(20)^{18} + 3(21)^2 (20)^{17} +\) \(\cdots + 20(21)^{19} =\) \(k(20)^{19}\), then \(k\) is equal to _____ :

Answer 1

Correct Answer: 400

We use the following series and simplifications: \[ S = (20)^{19} + 2(21)(20)^{18} + \cdots + 20(21)^{19} \] By calculating this series, we find that \(k = 400\).