Question

Suppose a plant puts out a new shoot, and that shoot has to grow two months before it is strong enough to support branching. If it branches every month after that at the growing point, write a recursion equation to describe number of branches after n months, B(n), and find its closed form, where B(1) = 1 and B(2) = 1.

Answer 1

A recursion equation is an equation that expresses each element of a sequence as a function of the preceding ones. after growing point i.e from 3rd month onward the no of branch will be 1 more in the next month, however for 1 and 2 branching will be just 1, this can be written in recersion equation as follows:

B(N) = 1 if N = 1 if N = 2 B(N-1) +1 iN > 3

a recursive fuction for this can be written as:

 void int numBranch(int numMonth){ if(numMonth == 1 || numMonth == 2){ return 1; } return numBranch(numMonth - 1) + 1; }