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A snail moves 1 mm in the first second and half the distance of the previous second in subsequent seconds. How long will it take for the snail to reach food 3 meters away?
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Solution: Step 1: Convert 3 meters to millimeters: 3 meters = 3000 mm Step 2: The snail's movement forms a geometric series: 1 + 0.5 + 0.25 + ... Step 3: The sum of an infinite geometric series is S = a / (1 - r), where a = 1 and r = 0.5 Step 4: Calculate the sum: S = 1 / (1 - 0.5) = 1 / 0.5 = 2 mm Step 5: Since the snail covers only 2 mm, it will never reach 3000 mm Step 6: Therefore, the snail will never reach its food
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