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# KCC's Quizzes : AQQ234 - Sum of even integers

The sum S of positive even integers starting from 2 to n (even) is described as :

S = 2 + 4 + 6 + 8 +… n where the last element n is even.

Questions:

1. What is the general formula (function of n) giving a such sum?
2. Give the sum with n = 5298

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[edited by: emassa at 1:29 PM (GMT -4) on 5 May 2023]
Parents
•   f(n=2m) = S = 2+4+6+ ... +2m    // by definition of f and change of variable, n= 2m
= 2*(1 + 2 + 3 + ... + m)   // common factor of 2
= 2(m*(m+1)/2) // by sum of the m first integers
= m(m+1)  // simplification
= (n/2)((n/2)+1) // by our definition of m

f(5298) = f( 2* 2649) = 2649*2650 = 7 019 850

•   f(n=2m) = S = 2+4+6+ ... +2m    // by definition of f and change of variable, n= 2m
= 2*(1 + 2 + 3 + ... + m)   // common factor of 2
= 2(m*(m+1)/2) // by sum of the m first integers
= m(m+1)  // simplification
= (n/2)((n/2)+1) // by our definition of m

f(5298) = f( 2* 2649) = 2649*2650 = 7 019 850

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