sum of even numbers from 2 to 100

Even numbers from 2 to 100

Even numbers are 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,    54, 56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100.

Now we will see the sum of elements:

Sum of first 2 even numbers: 2+4= 6

The above can be written as

Sum of first 2 even numbers: 2+4= 6= 2x3=2(2+1)

Sum of first 3 even numbers: 2+4+6= 12= 3(3+1)

Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1)

Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1)

Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1)

Sum of  even numbers from 2 to 100 = 2+4+6+8+10+. . . . .  50 numbers                                                                           = 50(50+1)

                                                                =50x51

                                                                =2550