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(1-1/4)(1-1/5)••••••(1-1/m) |
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Answer» 1 - 1/4 = 3/4 1 - 1/5 = 4/5 The numerator is always less by one. 1 - 1/(m-1) = (m-2)/(m-1) 1 - 1/m = (m-1)/m Given: (1 - 1/4)(1 - 1/5) ... (1 - 1/m) = 3/4 × 4/5 × ... × (m-2)/(m-1) × (m-1)/m Now we CLEARLY see the fractions cancelling out. It shows the answer is 3/m. |
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