These Ten-Year-Series (TYS) worked solutions with video explanations for 2007 A Level H2 Mathematics Paper 2 Question Q2 [Modified] are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2007 A Level H2 Math Paper 2 Question 2 [Modified]
A sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$, … is such that ${{u}_{1}}=1$ and
${{u}_{n+1}}={{u}_{n}}-\frac{2n+1}{{{n}^{2}}{{\left( n+1 \right)}^{2}}}$, for all $n\ge 1$.
(i)
Given that ${{u}_{n}}=\frac{1}{{{n}^{2}}}$, find $\sum\limits_{n=1}^{N}{\frac{2n+1}{{{n}^{2}}{{\left( n+1 \right)}^{2}}}}$.
[2]
(i) Given that ${{u}_{n}}=\frac{1}{{{n}^{2}}}$, find $\sum\limits_{n=1}^{N}{\frac{2n+1}{{{n}^{2}}{{\left( n+1 \right)}^{2}}}}$.
[2]
(ii)
Give a reason why the series in part (i) is convergent and state the sum to infinity.
[2]
(ii) Give a reason why the series in part (i) is convergent and state the sum to infinity.
[2]
(iii)
Use your answer to part (i) to find $\sum\limits_{n=2}^{N}{\frac{2n-1}{{{n}^{2}}{{\left( n-1 \right)}^{2}}}}$.
[2]
(iii) Use your answer to part (i) to find $\sum\limits_{n=2}^{N}{\frac{2n-1}{{{n}^{2}}{{\left( n-1 \right)}^{2}}}}$.
[2]
Suggested Video Solutions
Suggested Handwritten Solutions
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