If 1 + 1 - 2 2 · 1 + 1 - 4 2 · 3 + 1 - 6 2 · 5 + … … + 1 - 20 2 · 19 = α - 220 β , then an ordered pair α , β is equal to:

Step-by-step solution

S = 1 + ∑ r = 1 10 1 − 2 r 2 2 r − 1 = 1 + 10 − ∑ r = 1 10 8 r 3 − 4 r 2 = 11 − 8 10 × 11 2 2 − 4 10 × 11 × 21 6 = 11 − 2 110 2 − 140 × 11 = 11 − 22 1100 − 70 = 11 − 220 110 − 7 ∴ α − 220 β = 11 − 220 103 ∴ α = 11 ,   β = 103 α ,   β = 11 ,   103 .