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A paper sheet of 0.1 mm thickness is taken. Is cut in two and placed one above the other; is a thickness of 0.2 mm.
This roll is cut into two and put prte above the other; is a thickness of 0.4 mm.
The next time the same process takes place, the stack is at a thickness of 0.8 mm.
Assuming the role is of a size that allows for the same procedure 30 times, find the thickness that would have formed the bundle.

after n cuts, the thickness is 0.1 * 2^n mm.

so, evaluate when n=30.

To find the thickness of the bundle formed after performing the procedure 30 times, we need to understand the pattern of the thickness increase.

Let's analyze the thickness increase after each cut and stack operation:

- Initially, the paper sheet has a thickness of 0.1 mm.
- After the first cut and stack operation, the thickness becomes 0.2 mm.
- After the second cut and stack operation, the thickness becomes 0.4 mm.
- And so on...

We can observe that after each operation, the thickness doubles. So, we have a geometric progression with a common ratio of 2.

To find the thickness of the bundle after 30 operations, we can use the formula for the sum of a geometric progression:

Sum = (first term * (1 - common ratio^n)) / (1 - common ratio)

In this case, the first term is 0.1 mm, the common ratio is 2, and n is 30.

Plugging these values into the formula:

Sum = (0.1 * (1 - 2^30)) / (1 - 2)

Using a calculator, we can compute this expression to find the thickness of the bundle.