Home 2023 CJC Sigma Notation Tutorial Q7 Find the values of $A$, $B$ and $C$ such that for all values of $r$, $1+{{r}^{2}}=Aleft( r+2 right)left( r+1 right)+Bleft( r+1 right)+C$. Hence,
Home 2013 JJC P1 Q3 (i) Show that $frac{1}{sqrt{r+1}+sqrt{r}}=sqrt{r+1}-sqrt{r}$ for all $rin {{mathbb{Z}}^{+}}$. (ii) Hence find $sumlimits_{r=1}^{n}{frac{1}{sqrt{r+1}+sqrt{r}}}$. (iii) Deduce that $sumlimits_{r=1}^{n}{frac{1}{sqrt{r}}>2left( sqrt{n+1}-1 right)}$. Suggested Video Solutions Suggested Handwritten Solutions (i)
Home 2018 NYJC Promo Q6 (i) Show that $frac{1}{left( r-1 right)rleft( r+1 right)}$ can be expressed as $frac{A}{r-1}+frac{B}{r}+frac{C}{r+1}$, where $A$, $B$ and $C$ are constants to be determined. [1] (ii)
JJC P1 Q13 (i) Express $frac{1}{left( 2x+1 right)left( 2x+3 right)}$ in partial fractions. (ii) Hence, show that $sumlimits_{r=1}^{n}{frac{1}{left( 2r+1 right)left( 2r+3 right)}}=frac{n}{3left( 2n+3 right)}$. (iii) Deduce the sum of $frac{1}{3}+frac{1}{3left(
Home 2022 VJC J1 MYE Q10 A shrimp farmer cultivates marine shrimps in tanks. There are $4000$ marine shrimps in a tank at the start of January $2022$. At the
Home 2017 DHS Promo Q11 (a) The sum of the first $n$ terms of a sequence, ${{S}_{n}}$ , is a quadratic polynomial in $n$. It is given that the first
Home SAJC Sigma Notation Tutorial Q1 By considering $text{f}left( r right)-text{f}left( r+1 right)$ where $text{f}left( r right)=ln left( 1+frac{1}{r} right)$, find ${{S}_{n}}$, the sum of the first $n$ terms of
Home CJC APGP Tutorial Q5 Given that the geometric series $1+{{text{e}}^{-x}}+{{text{e}}^{-2x}}+…$has a sum to infinity, show that $x>0$. When $x=10$, write down the expressions for ${{S}_{n}}$, the sum to $n$
Home CJC APGP Tutorial Q4 (a) An arithmetic series has first term $1000$ and common difference $-1.4$ negative terms of the series. Find the sum of the first $20$ negative
2022 HCI J1 BT Q11 On $31$st December $2021$, Mei Qian bought a house and took a housing loan of $$500text{}000$ from a bank that charges interest at $1.8%$ per