No SIM 417 PM 53 K Back Viewer Undo 411 Why do we have to s

No SIM 4:17 PM 53% , K Back Viewer Undo 4.1.1 Why do we have to specify exactly two of the elements to begin with? Why not one or three? Before trying to say more about these numbers, let us consider another counting problem A staircase has n steps. You walk up taking one or two at a time. How many ways can you go up? 4.1 Fibonacci\'s Exercise 6 For n 1, there is only 1 way. For n = 2, you have 2 choices: take one step twice or two once. For n 3, you have 3 choices: three single steps, or one single followed by one double, or one double followed by one single. Now stop and try to guess what the answer is in general! If you guessed that the number of ways to go up on a stair with n steps is n, you are wrong. The next case, 4, gives 5 possibilities (111+1, 2+1+1, So instead of guessing, let\'s try the following strategy. Let\'s denote by Jn the answer. We try to figure out what Jn+1 is, assuming we know the value of J for 1 k

Solution

Here we have that by the definition of fibonacci series that its each next term is the sum of its just two previous terms. So we get its any of the term, when we have given its just previous two terms and that is why only, so that to get the third term directly, we always assume exactly two terms, first and second term so that third term can be calculated easily as sum of these two first terms and process continues accordingly.

Thus exactly two terms are required to begin with.

Answer