These Ten-Year-Series (TYS) worked solutions with video explanations for 2004 A Level H2 Mathematics Paper 1 Question 9 are suggested by Mr Gan. For any comments or suggestions please contact
2021 ACJC Promo Q12 Mrs Tan plans to start a business which requires a start-up capital of $$700,000$. She decided to first save $$200,000$ by depositing money every month into
2017 RVHS Promo Q5 A sequence ${{U}_{1}}$, ${{U}_{2}}$, ${{U}_{3}}$,… is defined by ${{U}_{n}}=frac{n}{{{text{e}}^{n}}}$. (i) Show that $frac{nleft( 1-text{e} right)+1}{{{text{e}}^{n+1}}}={{U}_{n+1}}-{{U}_{n}}$ . [1] (ii) Hence find $sumlimits_{r=1}^{n}{left( frac{rleft( 1-text{e} right)+1}{{{text{e}}^{r+1}}} right)}$ in
2017 NYJC Promo Q5 (i) By considering $tan left( A-B right)$ or otherwise, show that ${{tan }^{-1}}left( k+1 right)-{{tan }^{-1}}left( k right)={{cot }^{-1}}left( {{k}^{2}}+k+1 right)$ for $k>0$. [2] (ii)
2021 RI Promo Q4 A sequence ${{u}_{1}}$, ${{u}_{2}}$,${{u}_{3}}$, … is defined by ${{u}_{n}}=sumlimits_{r=1}^{n}{left( 2r+n+1 right)}$. Another sequence ${{v}_{1}}$, ${{v}_{2}}$, ${{v}_{3}}$, … is given by ${{v}_{n}}=frac{2}{{{u}_{n}}}$, where $nin {{mathbb{Z}}^{+}}$. (i) Find
2022 CJC Promo Q8 (i) Show that $frac{1}{r!}-frac{1}{left( r+1 right)!}=frac{r}{left( r+1 right)!}$. [1] (ii) Hence find $sumlimits_{r=1}^{N}{frac{r}{left( r+1 right)!}}$ in terms of $N$. [3] (iii) Explain why the series in
2022 NYJC Promo Q6 A sequence ${{u}_{1}}$, ${{u}_{2}}$, ${{u}_{3}}$,… is such that ${{u}_{r}}=frac{1}{r}-frac{1}{r+2}$ where $rge 1$. (i) Show that ${{u}_{r}}=frac{A}{rleft( r+2 right)}$ for a constant $A$ to be determined. Describe
2022 DHS Promo Q10 (a) By considering $4r-1=5r-left( 1+r right)$, use the method of differences to find $sumlimits_{r=1}^{n}{left( frac{4r-1}{{{5}^{r}}} right)}$. [4] (b) Hence find $sumlimits_{r=1}^{infty }{left( frac{4r-1}{{{5}^{r}}} right)}$, justifying your
2022 ASRJC P1 Q5 (i) By considering ${{u}_{n}}-{{u}_{n+1}}$, where ${{u}_{n}}=frac{1}{nleft( n+1 right)left( n+2 right)}$, find $sumlimits_{n=1}^{N}{frac{1}{nleft( n+1 right)left( n+2 right)left( n+3 right)}}$ in terms of $N$. [3] (ii) Hence or
2022 CJC Promo Q4 It is known that the ${{n}^{text{th}}}$ term of a sequence is given by ${{u}_{n}}=pleft( {{4}^{-n}} right)+qn+r$, where $p$, $q$ and $r$ are constants. It is given