Calculate in the most convenient way the value of the sum of numbers from 1 to 40.
| August 6, 2021 | education
To calculate the sum of numbers from 1 to 40 in the most convenient way, we regroup this sum as follows:
1 + 2 + 3 + … + 37 + 38 + 39 + 40 = (1 + 39) + (2 + 38) + (3 + 37) + … + (18 + 22) + (19 + 21 ) + 20 + 40.
The sum of each pair of numbers inside the brackets is 40. There are 19 such pairs in total. Therefore,
1 + 2 + 3 + … + 37 + 38 + 39 + 40 = 19 * 40 + 20 + 60 = 840.
Thus, the sum of the numbers from 1 to 40 is 840.
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