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r=1/√2
S∞=a/(1-r)
S∞=√2/(1-1/√2)
S∞=√2/(√2/√2 - 1/√2)
S∞=√2/[√2-1)/√2]
S∞=√2×√2/(√2-1)
S∞=2/(√2-1)
S∞=2(√2+1) / (√2-1)(√2+1)
S∞=(2√2+2) / 2-1
S∞=2√2+2