…in which you were asked to find a formula for , the nth triangular number.
We can use the same technique as before, but this time some variables will be involved instead of just numbers. That’s OK, variables don’t scare us!
So we know that twice the sum S is the same as adding together n copies of (n + 1).
And we have our formula: . A few examples are in order to check that it works. When n = 3, , and sure enough, . When n = 7, we have 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28, and . Awesome!