2070.82 – Mystery Function
First of all, . Then, further values of are given by
Under these circumstances, which of these formulas gives ?
(a) , (b) , (c) , (d) , (e) .
Of course we can just plug the first few integers into the five given formulas and see which works, but here is a more subtle way.
We start by calculating some values:
With each step we are adding one more number so should be something like . Let's calculate this sum:
So, we see that
The correct answer is (c). (That formula for the sum of the first n whole numbers is a handy one to know.)
For inquiring minds: what if isn't ? What if is, say, ? or ?