These Ten-Year-Series (TYS) worked solutions with video explanations for 2006 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
The function $\text{g}$ is defined by $\text{g}:x\mapsto \frac{3}{x},x>0$.
Find, in a similar form, ${{\text{g}}^{2}}$ and ${{\text{g}}^{35}}$.
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Verify that if
${{v}_{n}}=n\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$.
then
${{v}_{n+1}}-{{v}_{n}}=\left( m+1 \right)\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$.
[2]
Given now that
${{u}_{n}}=\left( n+1 \right)\left( n+2 \right)…\left( n+m \right)$,
find $\sum\limits_{n=1}^{N}{{{u}_{n}}}$ in terms of $m$ and $N$.
[3]
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