Express $\frac{2n+3}{n\left( n+1 \right)}$ in partial fractions and hence use the method of differen

Question

Express $\frac{2n+3}{n\left( n+1 \right)}$ in partial fractions and hence use the method of differences to find ${{\sum\limits_{n=1}^{N}{\frac{2n+3}{n\left( n+1 \right)}\left( \frac{1}{3} \right)}}^{n+1}}$ in terms of $N$. [4] Deduce the value of $\sum\limits_{n=1}^{\infty }{\frac{2n+3}{n\left( n+1 \right)}{{\left( \frac{1}{3} \right)}^{n+1}}}$ [1]

Accepted Answer

$\frac{1}{3}-\frac{1}{{{3}^{N+1}}\left( N+1 \right)};\frac{1}{3}$

N2007 P1 Q2 (FM 9234)

N2007 P1 Q2 (FM 9234)

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