11. find the sum of all natural numbers among the first one thousand numbers which are neither divisible by 2 or by 5
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Sum of numbers up to 1000 = (1/2)*1000*1001 = 500500
Sum of numbers divisible by 2 up to 1000 = 2*(1+2+...500) = 2*(1/2)*500*501 = 250500
Sum of numbers divisible by 5 up to 1000 = 5*(1+2+...200) = 5*(1/2)*200*201 = 100500
Sum of numbers divisible by both 2 and 5 up to 1000
= 10*(1+2+3+...100) = 10*(1/2)*100*101 = 50500
Required sum = 500500 - 250500 - 100500 + 50500 = 200000
Sum of numbers divisible by 2 up to 1000 = 2*(1+2+...500) = 2*(1/2)*500*501 = 250500
Sum of numbers divisible by 5 up to 1000 = 5*(1+2+...200) = 5*(1/2)*200*201 = 100500
Sum of numbers divisible by both 2 and 5 up to 1000
= 10*(1+2+3+...100) = 10*(1/2)*100*101 = 50500
Required sum = 500500 - 250500 - 100500 + 50500 = 200000
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