\(\left(\frac{1}{2} \cdot i + 1\right) \cdot \left(1 \cdot \frac{100}{\frac{1}{n}}\right)\)
- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
62.0
- Applied taylor to get
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
47.2
- Taylor expanded around 0 to get
\[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
47.2
- Applied simplify to get
\[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
17.1
- Using strategy
rm 17.1
- Applied div-inv to get
\[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\color{red}{\frac{i}{n}}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\color{blue}{i \cdot \frac{1}{n}}}\]
17.2
- Applied times-frac to get
\[\left(\frac{1}{2} \cdot i + 1\right) \cdot \color{red}{\frac{i \cdot 100}{i \cdot \frac{1}{n}}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \color{blue}{\left(\frac{i}{i} \cdot \frac{100}{\frac{1}{n}}\right)}\]
0.3
- Applied simplify to get
\[\left(\frac{1}{2} \cdot i + 1\right) \cdot \left(\color{red}{\frac{i}{i}} \cdot \frac{100}{\frac{1}{n}}\right) \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \left(\color{blue}{1} \cdot \frac{100}{\frac{1}{n}}\right)\]
0.3
