Finding Your Place (with Federico Ardila) - Numberphile Podcast 

It's apocryphal though

@@TheEternalVortex42 Some spot research finds that a version of the story was published as early as 1856 (a year after Gauss's death) as an example of the sort of fond memories Gauss had (and liked to share) of his childhood, though in that version it was just described as an arithmetic series (assuming I've correctly translated the German phrase). In 1877, there was a version where the series was given as 1 to 40. In 1906, the familiar 1-100 version had emerged. And in 1937, the series was described as "The problem was of the following sort, 81297 + 81495 + 81693 + ... + 100899, where the step from one number to the next is the same all along (here 198), and a given number of terms (here 100) are to be added." So the precise sequence is apocryphal (though 1-100 is pretty plausible) but the posing of some summation is at least reportedly based on Gauss's own first-hand account.