Example:

T(n) = 2T(n/2) + 1

Guess: T(n) = O(n)

Show: T(n) <= cn

Assume: T(n/2) <= cn/2

T(n) $\leq$ 2cn/2 + 1

= cn + 1 $\not\leq$ cn

But, we cannot remove the +1.