What is \(1 + 2 + 3 + 4 + 5\) all the way up to \(99 + 100\)?

1 + 2 + 3 + 4 + … + 99 + 100 = ( 1 + 100 ) + ( 2 + 99 ) + ( 3 + 98 ) + … ( 50 + 51 ) = 50 ⋅ 101 = 5050

Answered by konrad509 | 2024-06-10

You can use Gauss method...
Sum from 1 to n = [n(n+1)] / 2
So... 1 to 100 = [100(100+1)] / 2
= [100(101)] / 2 = [10100] / 2 = 5050

Answered by scarlettears102 | 2024-06-10

The sum of the integers from 1 to 100 is 5050. This can be done by pairing numbers from the start and the end of the series, which each sum to 101. There are 50 pairs, resulting in a total of 5050.
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Answered by konrad509 | 2025-02-12