Hope you find our articles enjoyable and have a great time learning math! 😁
2022 NJC P1 Q6 (i) By considering ${{u}_{k}}-{{u}_{k+1}}$, where ${{u}_{k}}=frac{1}{k!}$, find $frac{3}{4!}+frac{4}{5!}+frac{5}{6!}+…+frac{3n+2}{left( 3n+3 right)!}$ in terms of $n$. [4] (ii) Find $sumlimits_{r=5}^{3n+3}{frac{r-1}{r!}}$. Hence show that $sumlimits_{r=5}^{3n+3}{frac{3}{r!}<frac{1}{24}}$. [4] Suggested Video and
2022 TMJC P1 Q1 (i) Express $frac{3}{r}+frac{2}{r+1}-frac{5}{r+2}$ as a single fraction. [1] (ii) Hence find $sumlimits_{r=1}^{n}{frac{4r+3}{rleft( r+1 right)left( r+2 right)}}$. [3] (iii) Use your answer to part (ii) to find
HCI Sequence and Series Tutorial Q5 Given that $text{f}left( r right)=cos 2rtheta $, write $text{f}left( r right)-text{f}left( r+1 right)$ as a product of two sine functions. Use your result to
2007 HCI C1 Lecture Test Q6 [Modified] (i) Verify that for any non-zero real constant, $m$, $frac{1}{m}left( frac{1}{mr+1-m}-frac{1}{mr+1} right)=frac{1}{left( mr+1-m right)left( mr+1 right)}$. [1] (ii) Hence, show that $sumlimits_{r=1}^{n}{frac{1}{left( mr+1-m
2021 TJC P2 Q2 It is given that $text{f}left( r right)=frac{1}{r!}$ where $r$ is a positive integer. (i) Show that $text{f}left( r right)-text{f}left( r+1 right)=frac{r}{left( r+1 right)!}$. [1] (ii) The
2014 RVHS Promo Q2 The sum of the first $n$ terms of a progression is given by ${{S}_{n}}=1-{{text{e}}^{2n}}$. (i) Find ${{U}_{n}}$, the $n$th term of the progression. [2] (ii) Prove
These Ten-Year-Series (TYS) worked solutions with video explanations for 2020 A Level H2 Mathematics Paper 2 Question 2 are suggested by Mr Gan. For any comments or suggestions please contact
2012 DHS P2 Q4 A finite sequence ${{{a}_{n}}}$ has $50$ terms and is such that ${{a}_{n+1}}={{a}_{n}}+0.15$ for $n=1,,,2,,,3,…..,,49$ (i) Given that ${{a}_{50}}=99{{a}_{1}}$ show that ${{a}_{1}}=0.075$. [2] (ii) Find, without using
2016 CJC P1 Q6 (i) Given that $1-2r=A(r+1)+Br$, find the constants $A$ and $B$. [1] (ii) Use the method of differences to find $sumlimits_{r=1}^{n}{frac{1-2r}{{{3}^{r}}}}$. [3] (iii) Hence find the value
2010 ACJC P2 Q3 The sequence of real numbers ${{b}_{1}}$, ${{b}_{2}}$, ${{b}_{3}}$, …. is such that ${{b}_{1}}=4$ and ${{b}_{n}}={{b}_{n-1}}+2n$ for all $nin {{mathbb{Z}}^{+}}$, $nge 2$.Using the method of difference, show