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 _____ :
If \((20)^{19}\) + \(2(21)(20)^{18} + 3(21)^2 (20)^{17} +\) \(\cdots + 20(21)^{19} =\) \(k(20)^{19}\), then \(k\) is equal to _____ :
Updated On: Mar 21, 2025
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Correct Answer: 400
Solution and Explanation
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 \(k = 400\).
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