Question:
If
fraceˣ+e⁵xe³x=a₀+a₁x+a₂x²+a₃x³+⋯
then the value of 2a₁+2³a₃+2⁵a₅+⋯ is
If
fraceˣ+e⁵xe³x=a₀+a₁x+a₂x²+a₃x³+⋯
then the value of 2a₁+2³a₃+2⁵a₅+⋯ is
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Symmetric exponential functions cancel odd-powered terms.
Updated On: Mar 20, 2026
- \(e^2+e^{-2}\)
- \(e^4-e^{-4}\)
- \(e^4+e^{-4}\)
- 0
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The Correct Option is A
Solution and Explanation
fraceˣ+e⁵xe³x=e⁻2x+e²x
Maclaurin series contains only even powers.
Thus the given alternating weighted sum evaluates to:
e²+e⁻2
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