# [plt-scheme] errata HTDP 23.1

On Thu, 20 Jul 2006, wooks . wrote:
>* The text states that summing the first 10 even numbers should give 90 -
*>* the code provided gives 110.
*
Hi Wooks,
Are you sure? Just from doing this by hand, without the computer:
9
sum (2 * i)
i=0
9
= 2 * sum i
i=0
The second term in the product, the arithmetic series, is just the gauss
sum (n * (n+1) / 2). Knowing this, we get a closed form:
= 2 * 9(9+1) / 2
= 90
The sum of the first ten even numbers has to be 90, if we count zero as
the first even number.
Hmmm... Oh, I see now what you're talking about! The problem is more that
the comment in the contract needs the correction, rather than the code.
It says:
;; series-even : N -> number
;; to sum up the first n even numbers
but it should really be:
;; to sum up the first (n+1) even numbers
because (series-even 1) adds the first and second even numbers together.
Best of wishes!