Question

Help Please. The question is in the image.

Answer 1

• 2π

Explanation:

The length of semicircles:

• C = 2πr - full circle, the first one is half of this with r = 1, so it is π

The sequence is:

• π, 1/2π, 1/4π, ...

This is an infinite GP with the first term of π and common ratio 1/2.

The sum of the lengths of the semicircles is the sum of this sequence:

• S = a / (1 - r)
• S = π/(1 - 1/2) = π /(1/2) = 2π