Hello everyone, welcome to some reading.

Today our math teacher presented an problem when we were studying Geometric progression. The problem is the following:

A runner covers one meter in his first step, the next step will be 90% of the step before. After how many steps will he have "ran" 100 meters?

...

The problem can be formulated as this: $\displaystyle \frac { 1(0.9^x - 1) } { 0.9 -1 } = 100$

Working some with it we will end up with no good answer, we'll get the $\displaystyle x = \frac { 10^{(\log - 9)} } { 0.9 }$

Negative logarithms? We don't go there, yet.

As putting it as an equation don't work (for us newbies) we did some test-and-see. The calculators loose precision after 10 meters have been covered.

So, my teacher reasoned, the runner will never run 100 meters.

I disputed his answer and compared this problem with one of Zeno's paradoxes about a runner who's step first 1, then a half, then a quarter, and so on.

Will the runner ever cover 100 meters? My answer is yes, he will. But noone would agree with me.

What do you think of this problem?

Zeno's paradoxes - Wikipedia, the free encyclopedia
P.S. I got a russian to agree with me, it's always good to have a russian backing you up.