Adding

$2+4+6+\dots+100=2(1+2+3+\dots+50)=2*\frac{50*51}{2}=50*51=2550$

$n=50$

$a=2$

$b=2$

$S_{n}=\frac{n}{2}(2a+(n-1)b)$

$S_{50}=\frac{50}{2}(2 \times 2+(50-1)2)$

$S_{50}=25(4+98)$

$S_{50}=\boxed{2550}$

n(n+1)/4=2550

This is a sum of an arithmetic series.

= n(A1 + An) 2 = 50(2+100)/2 =50 (102)/2 =50*51 =2550

sum of even numbers from 1 to n = n(n+1) = 50 × 51 = 2550

sum of odd numbers from 1 to n = n²= 50² = 2500

the even number are paired number or the counting of 2 like 2,4,6,8,10....... so the sum of even numbers upto 100 is 2+4+6+8+10+..............................+100=2550