The function F(n) is defined recursively as F(1) = 2 and F(n) = F(n-1) + 1/2 for all integers n > 1. The correct calculation for F(101) involves recursively applying the function, leading to F(101) = F(100) + 1/2, rather than a direct arithmetic calculation. The final result for F(101) is 52, not 51, indicating a potential misinterpretation of the initial condition or a calculation error. Understanding the recursive nature of the function is crucial for arriving at the correct answer.
PREREQUISITESStudents in mathematics, particularly those studying sequences and recursion, as well as educators looking for examples of recursive function problems.
Yes, you are missing something huge.DrummingAtom said:Homework Statement
If F(1) = 2 and F(n) = F(n-1) + 1/2 for all integers n > 1, then F(101) = ?
Homework Equations
The Attempt at a Solution
F(101) = F(101-1) + 1/2 = 100 1/2
I know I'm missing something huge here because the answer in the book was 51. :-/ Thanks for your help.