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Because it's not a snail, but a bug.
And it won't even crawl for eternity, unless the burning stops extending, then yes.

More is added every minute than a bug can crawl. But if it were added millimeter by millimeter, it would eventually reach its destination.

Because it's not a snail, but a bug, lol.
And it won't even crawl for eternity, unless the burning stops extending, then yes.

Haha, good idea, Kosha. A bug isn't stupid; it should understand the futility of its efforts, unfold its wings, and just fly over.

It won't make it because the series diverges.

In general, Uranium gave the correct answer, and Lizard explained why. :D

In the first minute, the bug will crawl one hundredth of the distance, in the second minute, one two-hundredth, in the third minute, one three-hundredth, and so on, or a part of the distance will be covered: 1/100 + 1/200 + 1/300 + 1/400 + ...
If 1/100 is taken out of the parentheses, then the part of the cable covered by the bug will be (1/100) * (1/1 + 1/2 + 1/3 + 1/4 + ...). That is, 1/100 multiplied by the sum of the terms of the harmonic series. The harmonic series diverges, as Lizard correctly noted, so the bug will reach the end!!!

Added 3 minutes later

More is added each minute than the bug crawls.

At first, yes, but this addition will become smaller and smaller each time, and at some point, it will become less than the distance the bug crawls – less than one centimeter – and it will begin to approach the end of the cable.

If they diverge, how will they reach each other???:confused:

Ugh, yes, here's a different series (
That's why it will converge, Lizard. The divergence in the case of an increasing series indicates that it will take on any arbitrarily large value (sum).

Ugh, yes, here's a different series (
That's why it will eventually converge, Lizard. The divergence in the case of an increasing series indicates that it will take on an infinitely large value (sum).

The point is that this "infinite distance" is exactly what it needs to cover to reach the end. An infinite distance cannot be covered in a finite time. It can be reached if the series is convergent (a finite distance is covered in a finite time).:smile32:

If it converges to a sum greater than what we need. Yes. And it's an increasing series.
In this case, Hermit wrote the series himself. Although it diverges, it will reach the value we need after a finite number of terms, not at infinity.

If it does manage to crawl there, how long will it take? Since the initial size of the bundle is known, and the speed of the bug is also known, the time should be calculable.

With Achilles, 1/2^n
Here, 1/100*(1/n)
The first one, if expressed as a series, converges to a finite number. The second one diverges, roughly speaking, and converges to infinity. I didn't realize that the problems were different.
Let me estimate the time...

With Achilles, it's different. The series converges, and everything is fine.

If it crawls, how long will it take? Since the initial size of the whip is known and the speed of the bug is also known, the time should be calculable.

It can certainly be calculated, but this probably can only be done with a computer program. I think the formula for calculating the time can only be derived approximately. In general, we need to calculate how many terms of the harmonic series are needed so that their sum is equal to 100, and this will be the number of minutes. This time will probably be much longer than the age of our universe.

Approximately 2 * 10^43 minutes. The answer is approximate, but it's in that ballpark.
Mathematics, online version, helped.

1.6 * 10^43, to be even more precise.

Alright, who's next to make a wish? )