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RE: Math Contest #20 [2 SBI] <<<10 STEM for you if you solve the bonus problem>>>
- & 2. Using simple estimations one can show that the series is limited to [1,2]. 2/a_n has the property that for a_n>sqrt(2) the term will be <sqrt(2) and the other way round. Since you effectively get the mean between a_n and 2/a_n each iteration, this will bring you closer and closer to sqrt(2).
- Example: every number b>1 will definetly work and the series will converge to sqrt(b). a(n+1)=0.5(a(n) + b/a(n)) will give b as converging value.