In the fall term of 2015. Nick^2 took COMP 2804. Nick was always sitting in the

Question

In the fall term of 2015. Nick^2 took COMP 2804. Nick was always sitting in the back of the classroom and spent most of his tune eating bananas. Nick uses the following banana-buying-scheme: At the start of week 0, there are 2 bananas in Nick's fridge. For any integer n greaterthanorequalto 0. Nick does the following during week n: At the start of week n, Nick determines the number of bananas in his fridge and stores this number in a variable x. Nick goes to Jim's Banana Empire, buys x bananas, and puts them in his fridge. Nick takes n + 1 bananas out of his fridge and eats them during week n. For any integer n greaterthanorequalto 0, let B(n) be the number of bananas in Nick's fridge at the start of week n. Determine the value of B(n).

Explanation / Answer

The equation can be formulated as under:-

For Week No 0 or initial conditions Balance B(0) = 2 or B(n) = 2 for n=0

For Week 1 onwards Balance at Beginning of Next Week = Balance at Beginning of Previous week + Same number of Bananas bought from Jim's Banana Empire - (Week No +1)

OR

B(n+1) =B(n) +x- (n+1) where x= B(n)

Therefore B(n+1) = B(n) + B(n) - (n+1)

or B(n+1) = 2X B(n) -n + 1 -------- For n>=1

We have tabulated the results of tis equation and the solution terminates in the 2nd week beyond which no real world solution exists.

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