Math Problem Solver

$$\frac{125000}{1.25} + \frac{125000}{{1.25}^{2}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000 = \frac{311872}{5} = 62374.4$$

$$\begin{aligned}\frac{125000}{1.25} + \frac{125000}{{1.25}^{2}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000&=\frac{125000}{\frac{5}{4}} + \frac{125000}{{1.25}^{2}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=100000 + \frac{125000}{{1.25}^{2}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=100000 + \frac{125000}{{\left( \frac{5}{4} \right)}^{2}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=100000 + \frac{125000}{\frac{25}{16}} + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=100000 + 80000 + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=180000 + \frac{125000}{{1.25}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=180000 + \frac{125000}{{\left( \frac{5}{4} \right)}^{3}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=180000 + \frac{125000}{\frac{125}{64}} + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=180000 + 64000 + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=244000 + \frac{125000}{{1.25}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=244000 + \frac{125000}{{\left( \frac{5}{4} \right)}^{4}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=244000 + \frac{125000}{\frac{625}{256}} + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=244000 + 51200 + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=295200 + \frac{125000}{{1.25}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=295200 + \frac{125000}{{\left( \frac{5}{4} \right)}^{5}} + \frac{100000}{{1.25}^{6}} - 300000\\&=295200 + \frac{125000}{\frac{3125}{1024}} + \frac{100000}{{1.25}^{6}} - 300000\\&=295200 + 40960 + \frac{100000}{{1.25}^{6}} - 300000\\&=336160 + \frac{100000}{{1.25}^{6}} - 300000\\&=336160 + \frac{100000}{{\left( \frac{5}{4} \right)}^{6}} - 300000\\&=336160 + \frac{100000}{\frac{15625}{4096}} - 300000\\&=336160 + \frac{131072}{5} - 300000\\&=\frac{1811872}{5} - 300000\\&=\frac{311872}{5}\end{aligned}$$