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Question
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
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Solution
We have to find the sum of all the natural numbers that are divisible by 2 or 5
Required Sum = Sum of the natural numbers between 1 and 100 that are divisible by 2 + Sum of the natural numbers between 1 and 100 that are divisible by 5
− Sum of the natural numbers between 1 and 100 that are divisible by 2 and 5, i.e by 10
\[= \left( 2 + 4 + 6 + 8 + . . . + 98 \right) + \left( 5 + 10 + 15 + . . . + 95 \right) - \left( 10 + 20 + 30 + . . . + 90 \right)\]
\[ = \frac{50}{2}\left( 2 + 98 \right) + \frac{20}{2}\left( 5 + 95 \right) - \frac{10}{2}\left( 10 + 90 \right)\]
\[ = 2500 + 1000 - 500\]
\[ = 3000\]
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