Add all the numbers 1 through 100

Answer 1

To calculate the sum of 1–100 there is a trick

First calculate the sum of 1–10

It is

1+2+3+4+5+6+7+8+9+10 = 55

Similarly the sum of next ten numbers, that is from 11–20

It is

11+12+13+14+15+16+17+18+19+20 = 155

From the above two sums it is clear that the sum of next ten numbers numbers would be 255.

Similarly we would get 355,455,555,655,755,855,955.

Now adding all these sums, that is

55+155+255+355+455+555+655+755+855+955 = 5050.