$$\prod_{n=1}^{13}\left(1-\frac{4}{(2n-1)^2}\right)=?$$
You asked:
Evaluate the expression: \(\prod_{n = 1}^{13}{1 - \frac{4}{{\left( 2 n - 1 \right)}^{2}}}\)
MathBot Answer:
Evaluated
\(\displaystyle \prod_{n = 1}^{13}{1 - \frac{4}{{\left( 2 n - 1 \right)}^{2}}} = - \frac{27}{25} \)
Expanded
\[\prod_{n = 1}^{13}{1 - \frac{4}{{\left( 2 n - 1 \right)}^{2}}} = \prod_{n=1}^{13} \left(1 - \frac{4}{4 n^{2} - 4 n + 1}\right)\]