17. Consider the two expressions for π introduced previously—as limits of the sequences {πn} and {π'n in equations (5) and (6). We could combine them into the single expression
where a = 2 and 3, using the two equations (5) and (6), respectively. This leads to the conjecture that the above relation holds for all positive values of a. Verify or disprove the conjecture using specific values of a and testing the formula with your calculator. If you find that the conjecture is false, try to prove that the above relation holds only for the values a = 2 or 3. (In connection with this, see Problem 18.)
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