Pi - The most important but weird number

The famous Indian astronomer, Aryabhata, approximated the value of π\pi as 3.1416 3.1416 and then expressed it as a continued fraction of the form

a+1b+1c+1d, \large a+\frac{1}{b+\frac{1}{c+\frac{1}{d}}},

where a,b,c,d a,b,c,d are positive integers. Find a+b+c+d a+b+c+d.

Details and Assumptions:

  • Use the approximation π=3.1416 \pi = 3.1416 .

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