Solve F(101): Function Question Homework

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In summary, F(101) is equal to 51 when F(1) = 2 and F(n) = F(n-1) + 1/2 for all integers n > 1. The solution is found by recursively substituting the value of n into the equation until n = 101. It is important to note that the initial value of F(1) is 2 and not 1, as that would result in a different solution. By calculating a few more values of F(n), a pattern can be observed that leads to the solution of F(101) = 51.
  • #1
DrummingAtom
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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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  • #2
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.
 
  • #3
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?
 

FAQ: Solve F(101): Function Question Homework

What does "F(101)" mean in this question?

"F(101)" refers to the function that needs to be solved for the input value of 101. In other words, you need to find the output of the function when the input is 101.

How do I solve a function question?

To solve a function question, you need to follow the general steps of inputting the given value into the function, simplifying the expression, and finding the output value. It may also involve using mathematical operations and rules specific to the given function.

Can I use a calculator to solve the function?

It depends on the complexity of the function and the requirements of the question. In some cases, you may be allowed to use a calculator while in others, you may need to show your work and solve it manually.

Are there any tips for solving function questions?

Some tips for solving function questions include paying attention to the given instructions, checking for any restrictions on the input values, and using algebraic techniques to simplify the expression.

Is it possible to have multiple solutions for a function question?

Yes, it is possible to have multiple solutions for a function question, especially if the function is not one-to-one. In this case, the solutions may be in the form of a range of values or multiple distinct solutions.

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