\(\left({i}^2 \cdot 2500 - 100 \cdot 100\right) \cdot \frac{n}{50 \cdot i - 100}\)
- 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
\[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
17.2
- Applied taylor to get
\[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}} \leadsto 100 \cdot n + 50 \cdot \left(n \cdot i\right)\]
0.1
- Taylor expanded around 0 to get
\[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{100 \cdot n + 50 \cdot \left(n \cdot i\right)}\]
0.1
- Applied simplify to get
\[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{\left(i \cdot 50 + 100\right) \cdot n}\]
0.2
- Using strategy
rm 0.2
- Applied flip-+ to get
\[\color{red}{\left(i \cdot 50 + 100\right)} \cdot n \leadsto \color{blue}{\frac{{\left(i \cdot 50\right)}^2 - {100}^2}{i \cdot 50 - 100}} \cdot n\]
11.3
- Applied associate-*l/ to get
\[\color{red}{\frac{{\left(i \cdot 50\right)}^2 - {100}^2}{i \cdot 50 - 100} \cdot n} \leadsto \color{blue}{\frac{\left({\left(i \cdot 50\right)}^2 - {100}^2\right) \cdot n}{i \cdot 50 - 100}}\]
13.6
- Applied taylor to get
\[\frac{\left({\left(i \cdot 50\right)}^2 - {100}^2\right) \cdot n}{i \cdot 50 - 100} \leadsto \frac{\left(2500 \cdot {i}^2 - {100}^2\right) \cdot n}{i \cdot 50 - 100}\]
13.6
- Taylor expanded around 0 to get
\[\frac{\left(\color{red}{2500 \cdot {i}^2} - {100}^2\right) \cdot n}{i \cdot 50 - 100} \leadsto \frac{\left(\color{blue}{2500 \cdot {i}^2} - {100}^2\right) \cdot n}{i \cdot 50 - 100}\]
13.6
- Applied simplify to get
\[\frac{\left(2500 \cdot {i}^2 - {100}^2\right) \cdot n}{i \cdot 50 - 100} \leadsto \frac{\left(i \cdot i\right) \cdot 2500 - 100 \cdot 100}{\frac{i \cdot 50 - 100}{n}}\]
13.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\left(i \cdot i\right) \cdot 2500 - 100 \cdot 100}{\frac{i \cdot 50 - 100}{n}}} \leadsto \color{blue}{\left({i}^2 \cdot 2500 - 100 \cdot 100\right) \cdot \frac{n}{50 \cdot i - 100}}\]
13.5
