(4(5^(2n+1))-10(5^(2n-1)))/(2(5^(2n)))
You asked:
Evaluate the expression: \(\frac{4 \cdot {5}^{2 n + 1} - 10 \cdot {5}^{2 n - 1}}{2 \cdot {5}^{2 n}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{4 \cdot {5}^{2 n + 1} - 10 \cdot {5}^{2 n - 1}}{2 \cdot {5}^{2 n}} = \frac{5^{- 2 n} \left(- 10 \cdot 5^{2 n - 1} + 4 \cdot 5^{2 n + 1}\right)}{2} \)
Expanded
\[\frac{4 \cdot {5}^{2 n + 1} - 10 \cdot {5}^{2 n - 1}}{2 \cdot {5}^{2 n}} = 9\]
Factored
\[\frac{4 \cdot {5}^{2 n + 1} - 10 \cdot {5}^{2 n - 1}}{2 \cdot {5}^{2 n}} = 9\]