How do you find the total of 1to 10 1to 100 1to 1000?

Answer 1

To find the sum of 1 to 10, it helps to rearrange them, so instead of thinking of it like: 1 + 2 + . . . + 9 + 10, think like this: (1+10) + (2+9) + (3+8) + (4+7) + (5+6) = 11 + 11 + 11 + 11 + 11 = 5 x 11 = 55.

So you have 5, which is 10/2 times 11 which is 10+1.

Now to sum 1 to N, it is: (1 + N) + (2 + N-1) + (3 + N-2) + ... = (1+N) + (1+N) + ...., and you do that for N/2 times, so the answer is (1+N)*N/2.

So for:

• N = 100 : 101*100/2 = 5050,
• N=1000 : 1001*1000/2 = 500500.