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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
• <NOPE, I BELIEVE THIS IS INCORRECT.  I need to go back and spend more time on this.>

I'm noticing that the total given any n, call it T(n), is just n(n+1) as per below...

 n 1 2 3 4 5 2n 2 4 6 8 10 T(n) 2 6 12 20 30 n(n+1) 2 6 12 20 30

So, the formula is T(n) = n * (n+1)

For n = 5298, T(n) = 5298 * 5299 = 28,074,102

Not very scientific but I think it's correct.

• <NOPE, I BELIEVE THIS IS INCORRECT.  I need to go back and spend more time on this.>

I'm noticing that the total given any n, call it T(n), is just n(n+1) as per below...

 n 1 2 3 4 5 2n 2 4 6 8 10 T(n) 2 6 12 20 30 n(n+1) 2 6 12 20 30

So, the formula is T(n) = n * (n+1)

For n = 5298, T(n) = 5298 * 5299 = 28,074,102

Not very scientific but I think it's correct.

Children
• Hi Brian,