Thoughts Question on Constructive Induction

Question 1
Given the recurrence:
   T(0) = T(1) = 1
   T(n) = T(n-1) + T(n-2) + 1 for n>1
Find the smallest constant x>1 such that T(n)≤xn
using constructive induction.

   example solution on ELMS



Question 2
Given the recurrence:
   T(1) = 1
   T(n) = 1 + T(n-1) + 1 for n>1
Find the smallest constant x>1 such that T(n)≤xn
using constructive induction.