Find all sets of consecutive integers that add up to 1000.

Answer

There are total 8 such series:

1. Sum of 2000 numbers starting from -999 i.e. summation of numbers from -999 to 1000.

(-999) + (-998) + (-997) + ..... + (-1) + 0 + 1 + 2 + ..... + 997 + 998 + 999 + 1000 = 1000

2. Sum of 400 numbers starting from -197 i.e. summation of numbers from -197 to 202.

(-197) + (-196) + (-195) + ..... + (-1) + 0 + 1 + 2 + ..... + 199 + 200 + 201 + 202 = 1000

3. Sum of 125 numbers starting from -54 i.e. summation of numbers from -54 to 70.

(-54) + (-53) + (-52) + ..... + (-1) + 0 + 1 + 2 + ..... + 68 + 69 + 70 = 1000

4. Sum of 80 numbers starting from -27 i.e. summation of numbers from -27 to 52.

(-27) + (-26) + (-25) + ..... + (-1) + 0 + 1 + 2 + ..... + 50 + 51 + 52 = 1000

5. Sum of 25 numbers starting from 28 i.e. summation of numbers from 28 to 52.

28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 = 1000

6. Sum of 16 numbers starting from 55 i.e. summation of numbers from 55 to 70.

55 + 56 + 57 + 58 + 59 +60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 = 1000

7. Sum of 5 numbers starting from 198 i.e. summation of numbers from 198 to 202.

198 + 199 + 200 +201 + 202 = 1000

8. Sum of 1 number starting from 1000.

1000 = 1000

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