A Large Harmonic Mean

Algebra Level 4

The harmonic mean of the following numbers:

1×2×3×4××2013,1×2×3××2012×2014,1×2××2011×2013×2014,2×3×4××20141 \times 2 \times 3 \times 4 \times \ldots \times 2013, \\ 1 \times 2 \times 3 \times \ldots \times 2012 \times 2014, \\ 1 \times 2 \times \ldots \times 2011 \times 2013 \times 2014, \\ \vdots \\ 2 \times 3 \times 4 \times \ldots \times 2014

can be expressed in the form ab2014!,\frac{a}{b} 2014!, where aa and bb are coprime integers. Find a+ba+b.

×

Problem Loading...

Note Loading...

Set Loading...