Arithmetic and Geometric Series (tortoise and the hare)

[pbonnie]

Homework Statement

The question is attachedk

Homework Equations

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

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!

 

[pbonnie]

Picture

 

[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?

 

[eddybob123]

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

 

[Mark44]

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

Isn't that a contradiction of terms?