@chelsalina I only memorize the sum of the first n positive integers (which is n(n+1)/2). The sum of the first n odd (or even) integers is also fairly easy to derive.
Using this formula, the sum of the first 60 positive integers is 60*61/2 = 1830. This should take <15 seconds to multiply out (with or without a calculator).
If you don’t remember the formula (or wish to derive it), here is one way - Define S as follows:
S = 1 + 2 + 3 + … + 60
Then S = 60 + 59 + 58 + … + 1. Write out the two sums side-by-side and add them:
S = 1 + 2 + 3 + … + 60
S = 60 + 59 + … + 1
2S = 61 + 61 + … + 61 = 61*60
Then S = 61*60/2 = 1830.
Another tidbit: the sum of the first n squares (e.g. 1^2 + 2^2 + … + n^2) is fairly well known and is equal to n(n+1)(2n+1)/6. But deriving this is a little trickier.