Question

Find the sum of all positive integers less than 450

Answer 1

Answer:

Step-by-step explanation:

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First, consider all the positive integers less than 45. They range from 1 to 44, so their average must be 1+442=22.5. Since there are 44 of them, their sum must be 22.5⋅44=990

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Next consider all the multiples of 3

among this collection of integers. They range from 3 to 42 so their average must be 3+422=22.5. There are 14 such numbers, so their sum must be 22.5⋅14=315

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Since we know the sum of all those integers, and we know the sum of the multiples of three, the difference of those sums must be the sum of all those not divisible by three: 990−315=675

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