Carl Gauss’s Clever Trick

Carl’s Method:

1. Paired the numbers:
   1 + 100 = 101
   2 + 99 = 101
   3 + 98 = 101
   ...
   50 + 51 = 101
2. So, each pair gives 101, and there are 50 such pairs.
3. Total sum = 101 × 50 = 5050

Another way to understand it:
     1        2          3                     ............     99     100 (Hundred numbers)
+100     99       98                    ............       2         1    (Hundred numbers)
  101 + 101 + 101 +                 ............ + 101 + 101     (Hundred times)

But this total is double the actual sum, so divide by 2:

`"101 × 100" / "2"`= 5050

Conclusion:

• Carl Gauss found a quick trick to add numbers from 1 to 100.
• His method helps us add long number sequences easily.