Solutions Ch. 2, 1-11
Comment re #3: you should have come up with
(n-1) + (n-2) + ... + 3 + 2 + 1,
but you may not know that this sum equals n(n-1)/2. Here is why:
(It's like the old chestnut, asking how to count the number of chicken in
the yard. Answer: You count the legs and divide by 2. )
(n-1) + (n-2) + ... + 3 + 2 + 1 =
( (n-1) + (n-2) + ... + 3 + 2 + 1
+ 1 + 2 + ... (n-2)+(n-1) ) /2 =
( n + n + ... + n + n ) /2 =
(n-1)n/2
