An ant is crawling from the left end of a $4 \mathrm{~m}$ long rubber band towards the right end at a constant speed, covering exactly one meter per minute. After each minute, the horizontally placed rubber band, fixed at the left end, is uniformly stretched by one meter. In which minute does the ant reach the right end of the rubber band? The ant is considered point-like, the time taken to stretch the rubber band is negligible, and the rubber band can stretch indefinitely without breaking.
Solution. If we look at what fraction of the rubber band the ant has covered, this ratio does not change during the uniform stretching. Since in the first minute the band is $4 \mathrm{~m}$ long, the ratio of the distance covered is $\frac{1}{4}$. In the second minute, the band is $5 \mathrm{~m}$ long, the ratio is $\frac{1}{5}$, and so on, in the $i$-th minute it is $\frac{1}{i+3}$. By adding these fractions, we get the fraction of the band the ant has reached by the $i$-th minute. The minute in which the sum reaches or exceeds 1 is when the ant reaches the end.

Since

$$
\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}=\frac{2509}{2520}
$$

the ant reaches the right end of the band in the 7th minute.