N2007 P1 Q2 (FM 9234)
N2007 P1 Q2 (FM 9234)
5 marks
Past Year National Exams
Free
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]
Video Solution:
Default solution
Answer:\(\frac{1}{3}-\frac{1}{{{3}^{N+1}}\left( N+1 \right)};\frac{1}{3}\)
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