The immortal snail

Now the challenge for mathematicians :)

There is a gum length of 1 meter. A snail crawls along it. The speed of the cochlea is 1 cm per minute. She crawls from the left end of the gum to the right. At the end of each minute, the gum is stretched and its length is increased by 1 meter. "Stretching" occurs instantly and evenly along the entire length.
Question: Will the snail crawl to the right end of the gum?
It is clear that the snail lives forever and does not get tired.
Answer: crawl through about 5200000000000000000000000000000000 years