if N < 519383.0646430557

1. Started with
   \[\log \left(N + 1\right) - \log N\]
   30.9
2. Using strategy rm
   30.9
3. Applied diff-log to get
   \[\color{red}{\log \left(N + 1\right) - \log N} \leadsto \color{blue}{\log \left(\frac{N + 1}{N}\right)}\]
   28.6

if 519383.0646430557 < N

1. Started with
   \[\log \left(N + 1\right) - \log N\]
   59.7
2. Applied taylor to get
   \[\log \left(N + 1\right) - \log N \leadsto \left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}\]
   0.0
3. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}} \leadsto \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}}\]
   0.0
4. Applied simplify to get
   \[\color{red}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}} \leadsto \color{blue}{\frac{\frac{1}{N}}{N} \cdot \left(\frac{\frac{1}{3}}{N} - \frac{1}{2}\right) + \frac{1}{N}}\]
   0.0
5. Applied simplify to get
   \[\color{red}{\frac{\frac{1}{N}}{N} \cdot \left(\frac{\frac{1}{3}}{N} - \frac{1}{2}\right)} + \frac{1}{N} \leadsto \color{blue}{\frac{\frac{\frac{1}{3}}{N} - \frac{1}{2}}{{N}^2}} + \frac{1}{N}\]
   0.0