1. The problem statement, all variables and given/known data (1+n)^n≥ 5/2* n^n- 1/2* n^(n-1) for n≥2 2. Relevant equations i know I have to use this formula (1+x)^n=1+nx/1!+(n(n-1) x^2)/2!+⋯ 3. The attempt at a solution And you take x=n from my original inequality but after that I have no clue (1+n)^n=1+n/1! n+(n(n-1) n^2)/2!+⋯ but it seems very complicated !!