Quiz

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.