Solve F(101): Function Question Homework

[DrummingAtom]

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.

 

[Mark44]

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.

 

[niklaus]

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?