Problem description:

Cut watermelon with a knife, one knife can cut two pieces, two knives can cut four pieces, three knives can cut eight pieces, and four knives can cut 15 pieces.

How many pieces can you cut with 5 knives and 6 knives? Seven dollars? ..... 100?

Give formulas and ideas, and you can get extra points if you answer well.

Analysis:

Because cutting a knife is two pieces, which is the first power of 2.

Cutting two knives is four pieces, which is the square of 2.

Cutting three knives is eight pieces, which is the third power of 2.

Cutting four knives is sixteen pieces, which is the fourth power of two.

And so on, let the number of knives cut be n knives.

Then n knife is the n power of 2.