Given $\sum\limits_{r=1}^{n}{\frac{{{3}^{r}}(1-2r)}{r(r+1)}}=3-\frac{{{3}^{n+1}}}{n+1}$ , Deduce an

Question

Given $\sum\limits_{r=1}^{n}{\frac{{{3}^{r}}(1-2r)}{r(r+1)}}=3-\frac{{{3}^{n+1}}}{n+1}$ , Deduce an expression for $\sum\limits_{r=1}^{n-1}{\frac{{{3}^{r}}(1+2r)}{(r+1)(r+2)}}$. Deduce an expression for $\sum\limits_{r=1}^{n}{\frac{{{3}^{r}}(1+2r)}{(r+1)(r+2)}}$.

Accepted Answer

(i) $\frac{3^n}{n+1}-\frac32$; (ii) $\frac{3^{n+1}}{n+2}-\frac32$

IJC MYE P1 Q4 [Modified]

IJC MYE P1 Q4 [Modified]

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