By using the standard series, derive the first four non-zero terms of the power series expansion of

Question

By using the standard series, derive the first four non-zero terms of the power series expansion of ${{e}^{3{{x}^{2}}}}\ln (1-3x)$. Write down the range of values of $x$ for the expansion to be valid.

Accepted Answer

$\displaystyle e^{3x^2}\ln(1-3x)=-3x-\frac92x^2-18x^3-\frac{135}{4}x^4+O(x^5)$, valid for $\displaystyle -\frac13\le x<\frac13$.

Maclaurin Series and Power Series - Products and Quotients of Power Series

Maclaurin Series and Power Series - Products and Quotients of Power Series

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