2025 AMC 8 Problem 20

Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?

\textbf{(A)} \dfrac{4}{7} \qquad \textbf{(B)} \dfrac{3}{5} \qquad \textbf{(C)} \dfrac{2}{3} \qquad \textbf{(D)} \dfrac{3}{4} \qquad \textbf{(E)} \dfrac{7}{8}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.