The ancient Indian game of Chaturanga-from which the modern game of chess was apparently derived-was played on a board with 64 squares. certain folktale tells the story of a Raja who promised a reward of one grain of rice on the first square of the board, two grains on the second square, four on the third, and so on, doubling the number of grains on each successive square. (a) Write a recurrence relation for R(n), the number of grains of rice on the nth square. eBook R(n) = 1 2 (b) Compute R(64). (R-4) X • R(n-1) if n = 1 if n > 1 Assuming a grain of rice weighs 26 milligrams, how many kilograms of rice must be placed on the 64th square? (Round your answer to one decimal place.) X x 1014 kg 2

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.