Pascal's hockey shot

1111211331146411253002300126501263252600149501000 \begin{array}{c} 1 \end{array} \\ \begin{array}{cc} 1 & 1 \end{array} \\ \begin{array}{ccc} 1 & 2 & \color{#D61F06}{1}\end{array} \\ \begin{array}{cccc} 1 & 3 & \color{#D61F06}{3} & 1\end{array} \\ \begin{array}{ccccc} 1 & 4 & \color{#D61F06}{6} & 4 & 1\end{array} \\ \begin{array}{cccccc} \vdots & \hphantom{\vdots} & \vdots & \hphantom{\vdots} & \vdots \end{array}\\ \begin{array}{cccccc} 1 & 25 & \color{#D61F06}{300} & 2300 & 12650 & \cdots \end{array} \\ \begin{array}{ccccccc} 1 & 26 & 325 & 2600 & 14950 & \cdots & \hphantom{1000} \end{array} \\

Pascal's triangle is shown above for the 0th0^\text{th} row through the 4th4^\text{th} row, and parts of the 25th25^\text{th} and 26th26^\text{th} rows are also shown above.

What is the sum of all the 2nd2^\text{nd} elements of each row up to the 25th25^\text{th} row?


Note: The visible elements to be summed are highlighted in red.

Additional clarification: The topmost row in Pascal's triangle is the 0th0^\text{th} row. Then, the next row down is the 1st1^\text{st} row, and so on. The leftmost element in each row of Pascal's triangle is the 0th0^\text{th} element. Then, the element to the right of that is the 1st1^\text{st} element in that row, and so on.

×

Problem Loading...

Note Loading...

Set Loading...