if N < 36050.53017192879

1. Started with
   \[\log \left(N + 1\right) - \log N\]
   31.2
2. Using strategy rm
   31.2
3. Applied diff-log to get
   \[\color{red}{\log \left(N + 1\right) - \log N} \leadsto \color{blue}{\log \left(\frac{N + 1}{N}\right)}\]
   28.9

if 36050.53017192879 < 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
   \[\color{red}{\left(\frac{1}{3} \cdot \frac{1}{{N}^{3}} + \frac{1}{N}\right) - \frac{1}{2} \cdot \frac{1}{{N}^2}} \leadsto \color{blue}{\frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{N \cdot N}\right)}\]
   0.0
5. Applied taylor to get
   \[\frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{N \cdot N}\right) \leadsto \frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{{N}^2}\right)\]
   0.0
6. Taylor expanded around 0 to get
   \[\frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \color{red}{\frac{\frac{1}{2}}{{N}^2}}\right) \leadsto \frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \color{blue}{\frac{\frac{1}{2}}{{N}^2}}\right)\]
   0.0
7. Applied simplify to get
   \[\frac{1}{N} + \left(\frac{\frac{\frac{1}{3}}{N}}{N \cdot N} - \frac{\frac{1}{2}}{{N}^2}\right) \leadsto \left(\frac{1}{N} + \frac{\frac{\frac{1}{3}}{N}}{N \cdot N}\right) - \frac{\frac{\frac{1}{2}}{N}}{N}\]
   0.0

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8. Applied final simplification
9. Applied simplify to get
   \[\color{red}{\left(\frac{1}{N} + \frac{\frac{\frac{1}{3}}{N}}{N \cdot N}\right) - \frac{\frac{\frac{1}{2}}{N}}{N}} \leadsto \color{blue}{\left(\frac{1}{N} + \frac{\frac{1}{3}}{{N}^3}\right) - \frac{\frac{1}{2}}{N \cdot N}}\]
   0.0