Add the numbers from 1 to 100 by following the same steps you used in 1.

Summaation of a sequence

or see a smaller scale

from 1 to 10

notice

1+10=11

2+9=11

etc

5+6=11

10/2=5

there are 5 pairs

5*11=55

so

1 to 100

1+100=101

2+99=101

...

50+51=101

100/2=50

there ar 50 pairs

50 times 101=5050

the sum is 5050