Find the sum of all the natural numbers between 1 and 200 which are neither divisible by 2 nor by 5.
Asked by Athira Raj | 26th Jan, 2014, 03:40: PM
Expert Answer:
Sum of numbers up to 200 = (1/2)*200*201 = 20100
Sum of numbers divisible by 2 up to 200 = 2*(1+2+...+100) = 2*(1/2)*100*101 = 10100
Sum of numbers divisible by 5 up to 200 = 5*(1+2+...+40) = 5*(1/2)*40*41 = 4100
Sum of numbers divisible by both 2 and 5 up to 200
= 10*(1+2+3+...+20) = 10*(1/2)*20*21 = 2100
Required sum = 20100 - 10100 - 4100 + 2100 = 8000
Sum of numbers divisible by 2 up to 200 = 2*(1+2+...+100) = 2*(1/2)*100*101 = 10100
Sum of numbers divisible by 5 up to 200 = 5*(1+2+...+40) = 5*(1/2)*40*41 = 4100
Sum of numbers divisible by both 2 and 5 up to 200
= 10*(1+2+3+...+20) = 10*(1/2)*20*21 = 2100
Required sum = 20100 - 10100 - 4100 + 2100 = 8000
Answered by Vimala Ramamurthy | 27th Jan, 2014, 09:19: AM
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