\(\left(\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot 100\right) \cdot \frac{1}{i}\right) \cdot n\)
- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
62.0
- Applied taylor to get
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
47.4
- Taylor expanded around 0 to get
\[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
47.4
- Applied simplify to get
\[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{\frac{i}{n}}}\]
21.9
- Using strategy
rm 21.9
- Applied associate-/r/ to get
\[(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{red}{\frac{100}{\frac{i}{n}}} \leadsto (i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{blue}{\left(\frac{100}{i} \cdot n\right)}\]
21.7
- Applied associate-*r* to get
\[\color{red}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \left(\frac{100}{i} \cdot n\right)} \leadsto \color{blue}{\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{i}\right) \cdot n}\]
11.5
- Using strategy
rm 11.5
- Applied div-inv to get
\[\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{red}{\frac{100}{i}}\right) \cdot n \leadsto \left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{blue}{\left(100 \cdot \frac{1}{i}\right)}\right) \cdot n\]
11.6
- Applied associate-*r* to get
\[\color{red}{\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \left(100 \cdot \frac{1}{i}\right)\right)} \cdot n \leadsto \color{blue}{\left(\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot 100\right) \cdot \frac{1}{i}\right)} \cdot n\]
11.4
