mathematical distractions

i'm reading The Housekeeper and the Professor by Yōko Ogawa. first of all, i really like it! i haven't finished it yet, but i think it's touching. in addition, it features lots of maths! which admittedly can be distracting. the thing is that i understand extremely little of mathematics, but i'm so very interested, which is a dangerous combination.

for example, there was a bit about finding a trick to find the sum of all integers from 1 up to and including n. i thought about it and found a solution, which was adding 1 to n, then multiplying that with half of n. however, the characters in the book came up with a different solution, expressed in the following formula:

n(n – 1)/2 + n

however, my solution is this:

(n + 1)*(n/2)

but both of them gave the same result every time i tested them. therefore, i reasoned, they must be the same formula, and i spent the next two or so hours working through the steps to rewrite the book's formula into the form i came up with. i definitely learned this stuff in school, so it really shouldn't have taken this much effort, plus a peek at basic rules of reduction. but at least i did work it out. and they really are the same formula.

(basically what i mean to say is, i am a fucken nerd but also a dumbass)