2016 CJC P1 Q6
(i)
Given that $1-2r=A(r+1)+Br$, find the constants $A$ and $B$.
[1]
(ii)
Use the method of differences to find $\sum\limits_{r=1}^{n}{\frac{1-2r}{{{3}^{r}}}}$.
[3]
(iii)
Hence find the value of $\sum\limits_{r=1}^{\infty }{\frac{2-2r}{{{3}^{r}}}}$.
[4]
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