1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+.......

`1/(e^(3x))(e^x+e^(5x))=a_0+a_1x+a_2x^2+........=>2a_1+2^3a_3+2^5a_5+......=`

A

`e^(2)+e^(-2)`

B

`(e^(4)-e^(-4))/(2)`

C

`(e^(4)+e^(-4))`

D

`e^(4)+e^(-4)-(e^(4)+e^(-4))`

Text Solution

AI Generated Solution

To solve the problem, we need to evaluate the expression \( \frac{1}{e^{3x}(e^x + e^{5x})} \) and express it in the form of a power series. Then, we will find the sum \( 2a_1 + 2^3a_3 + 2^5a_5 + \ldots \). ### Step-by-Step Solution: 1. **Rewrite the Expression:** We start with the expression: \[ \frac{1}{e^{3x}(e^x + e^{5x})} ...

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