problem 1 if we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. the sum of these multiples is 23. find the sum of all the multiples of 3 or 5 below 1000.
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sum of all no. multiples of 3 below 1000 = sum of 3n
=3 (sum of n no.s) ,n=333
=3n(n+1)/2 ,n=333
after putting and solving =166833
by following the same,
sum of all no. multiples of 5 below 1000,
=5n(n+1)/2 ,n=200
=100500
as same ,sum of multiples of 15 =15n(n+1)/2 ,n=66
=33165
total sum=sum of multiple of 3 +sum of multiple of 5 - sum if multiples of 15
after putting and solving we get,
=234168
=3 (sum of n no.s) ,n=333
=3n(n+1)/2 ,n=333
after putting and solving =166833
by following the same,
sum of all no. multiples of 5 below 1000,
=5n(n+1)/2 ,n=200
=100500
as same ,sum of multiples of 15 =15n(n+1)/2 ,n=66
=33165
total sum=sum of multiple of 3 +sum of multiple of 5 - sum if multiples of 15
after putting and solving we get,
=234168
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