\(\left(n \cdot i\right) \cdot \left(\frac{50}{3} \cdot i + 50\right) + 100 \cdot n\)
- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
29.7
- Using strategy
rm 29.7
- Applied div-sub to get
\[100 \cdot \color{red}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \frac{1}{\frac{i}{n}}\right)}\]
29.5
- Applied simplify to get
\[100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \color{red}{\frac{1}{\frac{i}{n}}}\right) \leadsto 100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \color{blue}{\frac{n}{i}}\right)\]
29.5
- Applied taylor to get
\[100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \frac{n}{i}\right) \leadsto 100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right)\]
2.5
- Taylor expanded around 0 to get
\[\color{red}{100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right)} \leadsto \color{blue}{100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right)}\]
2.5
- Applied simplify to get
\[100 \cdot n + \left(\frac{50}{3} \cdot \left(n \cdot {i}^2\right) + 50 \cdot \left(n \cdot i\right)\right) \leadsto 50 \cdot \left(n \cdot i\right) + \left(n \cdot 100 + \left(i \cdot i\right) \cdot \left(\frac{50}{3} \cdot n\right)\right)\]
2.5
- Applied final simplification
- Applied simplify to get
\[\color{red}{50 \cdot \left(n \cdot i\right) + \left(n \cdot 100 + \left(i \cdot i\right) \cdot \left(\frac{50}{3} \cdot n\right)\right)} \leadsto \color{blue}{\left(n \cdot i\right) \cdot \left(\frac{50}{3} \cdot i + 50\right) + 100 \cdot n}\]
0.2
