Given that $1-2r=A(r+1)+Br$, find the constants $A$ and $B$.[1] Use the method of differe

Question

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

Accepted Answer

(i) $A=1$, $B=-3$ (ii) $\frac{n+1}{{{3}^{n}}}-1$(iii) $-\frac{1}{2}$

2016 CJC P1 Q6

2016 CJC P1 Q6

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