# Sums and Recurrences: Gotchas

In the previous post, we started looking into chapter `2.2`

of Concrete
Mathematics. This post lists a few gotchas found in the remaining part of the
chapter.

### Gotcha 1

Page 27. This factor is cleverly chosen to
make …

means **we assume** that .

### Gotcha 2

Page 27. To get `(2.10)`

, recall that . Hence

### Gotcha 4

Page 28. Let's see how exactly We can now subtract the second
equation from the first

.

### Gotcha 5

Page 28. We add a tiny but significant detail to the expansion of the *summation
factor*. It starts with substitution of and into
`(2.11)`

.

### Gotcha 6

Page 29. Substituting the *summation factor* into `(2.10)`

, for ,
, , we derive that

### Gotcha 7

Page 29. We finalize this journey through *gotchas* with a lucky number `7`

. And
we're looking into deriving the formula `(2.14)`

, which is even luckier.

And we're done here ðŸŽ‰ ðŸ¥³ !