3+$3*0.3^{5}/5$+$3*0.3^{10}/50$+$0.3^{7}/14$+$0.3^{2}/2$

asked by guest
on Oct 24, 2024 at 5:14 am



You asked:

Evaluate the expression: \(3 + \frac{3 \cdot {0.3}^{5}}{5} + \frac{3 \cdot {0.3}^{10}}{50} + \frac{{0.3}^{7}}{14} + \frac{{0.3}^{2}}{2}\)

MathBot Answer:

\[3 + \frac{3 \cdot {0.3}^{5}}{5} + \frac{3 \cdot {0.3}^{10}}{50} + \frac{{0.3}^{7}}{14} + \frac{{0.3}^{2}}{2} = \frac{10662658915029}{3500000000000} = 3.046473975722\overline{571428}\]

\[\begin{aligned}3 + \frac{3 \cdot {0.3}^{5}}{5} + \frac{3 \cdot {0.3}^{10}}{50} + \frac{{0.3}^{7}}{14} + \frac{{0.3}^{2}}{2}& = 3 + 3 \cdot \left(\frac{3}{10}\right)^{5} \cdot \frac{1}{5} + 3 \cdot \left(\frac{3}{10}\right)^{10} \cdot \frac{1}{50} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + 3 \cdot \frac{243}{100000} \cdot \frac{1}{5} + 3 \cdot \left(\frac{3}{10}\right)^{10} \cdot \frac{1}{50} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + 3 \cdot \frac{243}{500000} + 3 \cdot \left(\frac{3}{10}\right)^{10} \cdot \frac{1}{50} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + 3 \cdot \left(\frac{3}{10}\right)^{10} \cdot \frac{1}{50} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + 3 \cdot \frac{59049}{10000000000} \cdot \frac{1}{50} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + 3 \cdot \frac{59049}{500000000000} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + \frac{177147}{500000000000} + \left(\frac{3}{10}\right)^{7} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + \frac{177147}{500000000000} + \frac{2187}{10000000} \cdot \frac{1}{14} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + \frac{177147}{500000000000} + \frac{2187}{140000000} + \left(\frac{3}{10}\right)^{2} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + \frac{177147}{500000000000} + \frac{2187}{140000000} + \frac{9}{100} \cdot \frac{1}{2}\\& = 3 + \frac{729}{500000} + \frac{177147}{500000000000} + \frac{2187}{140000000} + \frac{9}{200}\\& = \frac{1500729}{500000} + \frac{177147}{500000000000} + \frac{2187}{140000000} + \frac{9}{200}\\& = \frac{1500729177147}{500000000000} + \frac{2187}{140000000} + \frac{9}{200}\\& = \frac{10505158915029}{3500000000000} + \frac{9}{200}\\& = \frac{10662658915029}{3500000000000}\end{aligned}\]

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