MathDB

11

Part of 1988 Irish Math Olympiad

Problems(1)

Determining Decimal Expansion without Division

Source: 1988 IrMO Paper 1 Problem 11

9/28/2017
If facilities for division are not available, it is sometimes convenient in determining the decimal expansion of 1/a1/a, a>0a>0, to use the iteration x_{k+1}=x_k(2-ax_k),     k=0,1,2,\dots , where x0x_0 is a selected “starting” value. Find the limitations, if any, on the starting values x0x_0, in order that the above iteration converges to the desired value 1/a1/a.