Guess about Gauss

Okay. Here is the anecdote that John C Wright, innumerate, found in MEN OF MATHEMATICS:

here’s a popular story that Gauss, mathematician extraordinaire, had a lazy teacher. The so-called educator wanted to keep the kids busy so he could take a nap; he asked the class to add the numbers 1 to 100.

Gauss approached with his answer: 5050. So soon? The teacher suspected a cheat, but no. Manual addition was for suckers, and Gauss found a formula to sidestep the problem:

Sum from 1 to n = {n(n+1)}/2

Sum from 1 to 100 = {100(100+1)}/2 = (50)(101) = 5050

Shamelessly stealing the anecdote from real life, and assuming my hero could figure out the same trick, here is the way I describe it in my book:

Menelaus had simply folded the number line in half in his mind, noticed that every one of the fifty pairs added up to one hundred one, and multiplied one hundred one by fifty.

But a reader said

Found mistake in sum 1-100. I’m probably the 5050′th person to mention that. The correct answer is 101×50 not 101×50 – 50.

So … is he simply wrong here? From the balance of his comments, I don’t have much faith in the gentleman’s reading comprehension, but I also know I am the worst student of mathematics the human race has ever produced, so I’d like a second opinion.

Some kind reader set me straight, please.

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