# Arithmetic and Geometric Series (tortoise and the hare)

1. Mar 15, 2013

### pbonnie

1. The problem statement, all variables and given/known data
The question is attachedk

2. Relevant equations
Sn = n/2[2a+(n-1)d]
Sn = (a x (1-r^n))/1-r

3. The attempt at a solution
I already found the general formulas:
Tortoise:
Sn = n/2(40)
Hare:
Sn = (1000 x [1-0.5^n])/0.5

And I know that there tortoise will finish the race in 100 minutes. But I don't think the hare ever finishes the race? This is the work I did so far trying to solve for the hare:
2000 = (1000(1-0.5^n))/0.5
1000 = 1000(1-0.5^n)
1 = 1-0.5^n
2 = 0.5^n
But 0.5 the the power of anything can never equal 2?

Thank you!

2. Mar 15, 2013

### pbonnie

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3. Mar 15, 2013

### pbonnie

Correction* 0 = 0.5^n
Is that the solution? The hare can never finish the race because no matter what value n is, it can never equal 0?

4. Mar 15, 2013

### eddybob123

Correction: it will eventually finish, but takes an infinite amount of time

5. Mar 15, 2013

### Staff: Mentor

Isn't that a contradiction of terms?