sum of integers - 2

Algebra Level pending

Find the sum of all positive integers less than 50000 50000 that are divisible by 11 11 .


The answer is 113638635.

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1 solution

The numbers form an arithmetic progression with first term of 11 11 and common difference of 11 11 . To find for the number of terms we divide 50000 50000 by 11 11 and it is approximately 4545.454545 4545.454545 , so the number number of terms is 4545 4545 . To get the last term we multiply 4545 4545 by 11 11 and that is 49995 49995 . So the sum of the progression is

s = n 2 ( a 1 + a n ) = 4545 2 ( 11 + 4995 ) = 113638635 s=\dfrac{n}{2}(a_1+a_n)=\dfrac{4545}{2}(11+4995)=\boxed{113638635}

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