\(\frac{\frac{100}{1} + \left(\frac{100}{1} \cdot i\right) \cdot \left(i \cdot \frac{1}{6} + \frac{1}{2}\right)}{\frac{1}{n}}\)
- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
61.8
- Using strategy
rm 61.8
- Applied div-inv to get
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{red}{\frac{i}{n}}} \leadsto 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\color{blue}{i \cdot \frac{1}{n}}}\]
61.8
- Applied *-un-lft-identity to get
\[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{i \cdot \frac{1}{n}} \leadsto 100 \cdot \frac{\color{blue}{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}{i \cdot \frac{1}{n}}\]
61.8
- Applied times-frac to get
\[100 \cdot \color{red}{\frac{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{i \cdot \frac{1}{n}}} \leadsto 100 \cdot \color{blue}{\left(\frac{1}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\right)}\]
62.0
- Applied associate-*r* to get
\[\color{red}{100 \cdot \left(\frac{1}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\right)} \leadsto \color{blue}{\left(100 \cdot \frac{1}{i}\right) \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}}\]
62.0
- Applied simplify to get
\[\color{red}{\left(100 \cdot \frac{1}{i}\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}} \leadsto \color{blue}{\frac{100}{i}} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\]
62.0
- Applied taylor to get
\[\frac{100}{i} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}} \leadsto \frac{100}{i} \cdot \frac{\frac{1}{2} \cdot {i}^2 + \left(i + \frac{1}{6} \cdot {i}^{3}\right)}{\frac{1}{n}}\]
20.2
- Taylor expanded around 0 to get
\[\frac{100}{i} \cdot \frac{\color{red}{\frac{1}{2} \cdot {i}^2 + \left(i + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{1}{n}} \leadsto \frac{100}{i} \cdot \frac{\color{blue}{\frac{1}{2} \cdot {i}^2 + \left(i + \frac{1}{6} \cdot {i}^{3}\right)}}{\frac{1}{n}}\]
20.2
- Applied simplify to get
\[\frac{100}{i} \cdot \frac{\frac{1}{2} \cdot {i}^2 + \left(i + \frac{1}{6} \cdot {i}^{3}\right)}{\frac{1}{n}} \leadsto \frac{100}{i} \cdot \frac{\left({i}^3 \cdot \frac{1}{6} + \left(i \cdot i\right) \cdot \frac{1}{2}\right) + i}{\frac{1}{n}}\]
20.2
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{100}{i} \cdot \frac{\left({i}^3 \cdot \frac{1}{6} + \left(i \cdot i\right) \cdot \frac{1}{2}\right) + i}{\frac{1}{n}}} \leadsto \color{blue}{\frac{\frac{100}{1} + \left(\frac{100}{1} \cdot i\right) \cdot \left(i \cdot \frac{1}{6} + \frac{1}{2}\right)}{\frac{1}{n}}}\]
5.6
