KCC's Quizzes : AQQ234 - Sum of even integers

  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

Bravo Michel, you get it!