For integers n and r, let (nr)={nCr,if n≥r≥00,otherwise The maxim – InterviewSolution

1.	For integers n and r, let (nr)={nCr,if n≥r≥00,otherwise The maximum value of k for which the sum k∑i=0(10i)(15k−i)+k+1∑i=0(12i)(13k+1−i) exists, is equal to
Answer» For integers $n$ and $r,$ let $(\begin{matrix} n r \end{matrix}) = {\begin{matrix} ^{n} C_{r}, & if n \geq r \geq 0 0, & otherwise \end{matrix}$ The maximum value of $k$ for which the sum $k \sum i = 0 (\begin{matrix} 10 i \end{matrix}) (\begin{matrix} 15 k - i \end{matrix}) + k + 1 \sum i = 0 (\begin{matrix} 12 i \end{matrix}) (\begin{matrix} 13 k + 1 - i \end{matrix})$ exists, is equal to

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