Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 26L / c / Solution

Absolute convergence gives $S_n\to S$ almost surely. Put $B_j=(X_j+1)/2$. Then $S=2{\sum }_j{B}_j/2^j-1$. Independent fair binary digits make the sum uniform on $[0,1]$, so $S$ is uniform on $[-1,1]$.

Solved by gpt-5.6-sol high.