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Solution

Sum of numbers divisible by 2 up to 100: $2 + 4 + \dots + 100 = 2(1 + 2 + \dots + 50) = 2 \times \frac{50 \times 51}{2} = 2550.$ Sum of numbers divisible by 5 up to 100: $5 + 10 + \dots + 100 = 5(1 + 2 + \dots + 20) = 5 \times \frac{20 \times 21}{2} = 1050.$ Sum of numbers divisible by both 2 and 5 (i.e., by 10): $10 + 20 + \dots + 100 = 10(1 + 2 + \dots + 10) = 10 \times 55 = 550.$ Required sum = $2550 + 1050 - 550 = 3050.$