Expand $(1-3x)^{-1}$ and find the greatest coefficient. Just wondering if there would be need to factorise before proceeding just as in the case of $(2-3x)^{-3}$. Response will be appreciated.
expanding exponential of inverse
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$\begingroup$
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0What do you mean by expanding? Taylor Series? – 2017-02-03
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0If you look for the partial fraction expansion, I'm afraid you cannot expand $\frac{1}{1-3x}$. – 2017-02-03
1 Answers
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Using Binomial series OR Infinite Geometric Series
$$(1-3x)^{-1}=\sum_{r=0}^\infty(3x)^r$$ for $|3x|<1$
So, the coefficient of $r$th term $T_r=3^r$
$$\implies\dfrac{T_{n+1}}{T_n}=3$$
Clearly, the coefficient are ever increasing.