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पूर्णांकों $n$ तथा $r$ के लिए,
माना $\left(\begin{array}{l} n \\ r \end{array}\right)=\left\{\begin{array}{cc}{ }^{ n } C _{ r }, & \text { if } n \geq r \geq 0 \\ 0, & \text { otherwise }\end{array}\right.$ तो $k$ का वह अधिकतम मान, जिसके लिए, योगफल $\sum_{i=0}^{k}\left(\begin{array}{c}10 \\ 1\end{array}\right)\left(\begin{array}{c}15 \\ k-i\end{array}\right)+\sum_{i=0}^{k+1}\left(\begin{array}{c}12 \\ i\end{array}\right)\left(\begin{array}{c}13 \\ k+1-i\end{array}\right)$ का अस्तित्व है, ........... |
Not define
$24$
$36$
$20$
Solution
$\sum_{i=0}^{k}\left(\begin{array}{c}10 \\ i\end{array}\right)\left(\begin{array}{c}15 \\ k-i\end{array}\right)+\sum_{i=0}^{k+1}\left(\begin{array}{c}12 \\ i\end{array}\right)\left(\begin{array}{c}13 \\ k+1-i\end{array}\right)$
${ }^{25} C _{ k }+{ }^{25} C _{ k +1}$
${ }^{26} C _{ k +1}^{ }$
as ${ }^{ n } C _{ r }$ is defined for all values of $n$ as will as r so ${ }^{26} C _{ k +1}$ always exists
Now $k$ is unbounded so maximum value is not defined.
