JEE Math Practice Question
Suppose \[ \operatorname{det}\left[\begin{array}{cc} \sum_{k=0}^{n} k & \sum_{k=0}^{n}{ }^{n} C_{k} k^{2} \\ \sum_{k=0}^{n}{ }^{n} C_{k} k & \sum_{k=0}^{n}{ }^{n} C_{k} 3^{k} \end{array}\right]=0 \] holds for some positive integer $n$. Then what does $\sum_{k=0}^{n} \frac{{ }^{n} C_{k}}{k+1}$?
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