Çözüldü Exponential Numbers in Fractals (8th Grade)

A fractal is constructed using semicircles. Step 1 consists of a single large semicircle. In Step 2, two smaller semicircles are drawn such that one endpoint of each new diameter coincides with an endpoint of the original semicircle's diameter. In each subsequent step, two smaller semicircles are added to the open endpoints of every semicircle drawn in the previous step. How many total semicircles have been drawn by the end of the 11th step?

Step 1: 1 semicircle
Step 2: 1 + 2 = 3 semicircles
Step 3: 1 + 2 + 4 = 7 semicircles
Step n: Total = 2^n - 1
Step 11: Total = 2^11 - 1 = (2^10)·2 - 1 = 1024·2 - 1 = 2048 - 1 = 2047 semicircles.

Notes:
1. An 8th grade student is already expected to know the exact value of 2^10 by heart.
2. This problem can also be solved by directly applying the formula for the sum of the certain amount of consecutive terms in the related geometric series: 2^0 + 2^1 + 2^2 + ... + 2^11 = S(11) = 2^0·(2^11 - 1) / (2 - 1) = 2047

Source (Turkish):
"8. Sınıf Matematik Soru Bankası", (SBS Hazırlık), AnaFen Dersanesi, Mayıs 2009, Sayfa 9, Soru 1
(6. adımdaki yarım çember sayısı sorulmuş.)