Find the sum of all natural numbers from 1 to 1000 which are not divisible by 5
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Answer:
400000
Step-by-step explanation:
The sum of the natural numbers from 1 to 1000 is
1 + 2 + ... + 1000
= 1000 × ( 1000 + 1 ) / 2
= 500 × 1001
The sum of the natural numbers from 1 to 1000 that are divisible by 5 is
5 + 10 + ... + 1000
= 5 × ( 1 + 2 + ... + 200 )
= 5 × 200 × ( 200 + 1 ) / 2
= 500 × 201
The sum of the natural numbers from 1 to 1000 that are not divisible by 5 is then the difference of these:
500 × 1001 - 500 × 201
= 500 × ( 1001 - 201 )
= 500 × 800
= 400000
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