using this technique is inefficient in this case in factit takes an exponential number of calls to compute the kth fibonacci number in this way specificallylet denote the number of calls performed in the execution of binaryfib(kthenwe have the following values for the 'sn if we follow the pattern forwardwe see that the number of calls more than doubles for each two consecutive indices that isn is more than twice is more than twice is more than twice and so on thusn / which means that binaryfib(kmakes number of calls that are exponential in in other wordsusing binary recursion to compute fibonacci numbers is very inefficient computing fibonacci numbers via linear recursion the main problem with the approach abovebased on binary recursionis that the computation of fibonacci numbers is really linearly recursive problem it is not good candidate for using binary recursion we simply got tempted into using binary recursion because of the way the kth fibonacci numberf depends on the two previous valuesf - and - but we can compute much more efficiently using linear recursion in order to use linear recursionhoweverwe need to slightly redefine the problem one way to accomplish this conversion is to define recursive function that computes pair of consecutive fibonacci numbers ( , - using the convention - then we can use the linearly recursive algorithm shown in code fragment