Hi all-
I need to see the steps to get
(1- 1/2 + 1/2*e^t)^25 * (1- 1/2 + 1/2*e^(-t))^25 * e^(25t)
to be (1- 1/2 + 1/2*e^t)^50
Can anyone help, i am having trouble seeing how?
Brian
Probably there is a typo in your question because 1 - 1/2 = 1/2 . I don't understand why you didn't simplify this sum first.
Nevertheless I show you what to do:
$\displaystyle \left(1-\frac12 + \frac12 \cdot e^t\right)^{25} \cdot \left(1-\frac12 + \frac12 \cdot e^{-t}\right)^{25} \cdot e^{25t} = \left(\frac12 + \frac12 \cdot e^t\right)^{25} \cdot \left(e^t \left(\frac12 + \frac12 \cdot e^{-t}\right) \right)^{25} $ $\displaystyle = \left(\frac12 + \frac12 \cdot e^t\right)^{25} \cdot \left(\frac12 \cdot e^t+ \frac12 \right)^{25} = \left(\frac12 + \frac12 \cdot e^t\right)^{50}$