MathDB
Putnam 1957 B2

Source: Putnam 1957

July 1, 2022
Putnamiterated functionlimit

Problem Statement

In order to determine 1A\frac{1}{A} for A>0A>0, one can use the iteration Xk+1=Xk(2−AXk),X_{k+1}=X_{k}(2-AX_{k}), where X0X_0 is a selected starting value. Find the limitation, if any, on the starting value X0X_0 so that the above iteration converges to 1A.\frac{1}{A}.
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