Solve F(101): Function Question Homework

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To solve for F(101) given F(1) = 2 and F(n) = F(n-1) + 1/2, the correct approach involves calculating each function value step-by-step rather than jumping to conclusions. The initial calculations should start from F(2) and continue to F(101) to identify a pattern. The mistake lies in assuming F(101) equals 100 + 1/2 instead of properly evaluating F(100) first. The expected answer is 51, indicating a misunderstanding of the function's recursive nature. A thorough calculation of the first few values is essential to grasp the function's progression.
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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.
 
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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.
Yes, you are missing something huge.
F(101) = F(101-1) + 1/2 = F(100) + 1/2, not 100 + 1/2.

Start by calculating F(2), F(3), and a few more to see if you can get an idea of what's happening here.
 
What is F(2)? F(3)? maybe you'll see a pattern... I would get 52 in the end though, are you sure it's not F(1)=1?
 

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