Question 923653
Sum of all consecutive integers: 

{{{sum=(n(n+1))/2}}} 


SUM OF {{{EVEN}}} NUMBERS:

Formula: {{{N(N+1)}}}

How to Find {{{N = (First_Even + Last_Even)/2 -1}}}

in your case: 

{{{2+4+6}}}+...+{{{100}}} 

find how many even numbers we have from {{{1}}} to {{{100}}}

{{{N = (2+100)/2- 1 = 50 }}}

go to  {{{N(N+1)}}} and find a sum of first {{{50}}} positive {{{even}}} integers => {{{N(N+1)=(50)(51) =highlight( 2550) }}}