Sequence and series

Timothy Gan

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2015 TJC P2 Q2 [Modified]

2015 TJC P2 Q2 [Modified] (b) Mr Tan set aside $$80,000$ for his two sons. On the first day of the year that his sons turned $7$ and $17$ years

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2010 NYJC Promo Q5 [Modified]

2010 NYJC Promo Q5 [Modified] (i) Using partial fractions, show that $sumlimits_{n=1}^{N}{frac{1}{nleft( n+1 right)left( n+2 right)}=frac{1}{4}-frac{1}{2left( N+1 right)left( N+2 right)}}$. [4] (ii) Deduce the value of $sumlimits_{n=2}^{infty }{frac{1}{nleft( n+1 right)left(

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2007 VJC P1 Q6

2007 VJC P1 Q6 The positive numbers ${{x}_{n}}$ satisfy the equation ${{x}_{n+1}}=sqrt{{{x}_{n}}+3}$, for $n=1$, $2$, $3$, ā€¦ As $nto infty $, ${{x}_{n}}to alpha $. (i) Find the exact value of

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2007 SRJC P1 Q4

2007 SRJC P1 Q4 (a) A sequence $left{ {{x}_{n}} right}$ of positive numbers is defined as ${{x}_{n,+1}}=frac{{{x}_{n}}^{2}+2}{2{{x}_{n}}+3}$ for $nin {{mathbb{Z}}^{+}}$. The sequence $left{ {{x}_{n}} right}$ converges to a number $lambda

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2024 ACJC Recurrence Relations Tutorial Q5

2024 ACJC Recurrence Relations Tutorial Q5 For the following sequence, write down their ${{2}^{text{nd}}}$ and ${{3}^{text{rd}}}$ terms, and determine whether the sequences are convergent. If they are, write down their

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2022 YIJC Promo Q4

2022 YIJC Promo Q4 (a) Express $frac{5r+8}{rleft( r+1 right)left( r+2 right)}$ in partial fractions. [2] (b) Hence, find $sumlimits_{r=,,1}^{n}{frac{5r+8}{rleft( r+1 right)left( r+2 right)}}$, giving your answer in the form $M-frac{P}{n+1}-frac{Q}{n+2}$,

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2022 RI Promo Q4

2022 RI Promo Q4 (i) Find $sumlimits_{r=1}^{n}{frac{1}{left( r+1 right)left( r+3 right)}}$, where $nge 3$. (There is no need to express your answer as a single algebraic fraction.) [5] (ii) Explain

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2022 ACJC Promo Q11

2022 ACJC Promo Q11 Antonio used a credit card to buy a diamond ring to propose to his girlfriend. On 1st October 2022, he charged $$7500$ to the credit card.

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2022 YIJC Promo Q8

2022 YIJC Promo Q8 An arithmetic series has first term $a$ and common difference $d$, where $a>0$ and $d$ is non-zero. The first, eighth and thirteenth terms of the arithmetic

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2022 CJC Promo Q2

2022 CJC Promo Q2 The second, fifth and tenth term of an arithmetic series with non-zero common difference are the first three terms of a geometric series respectively. (i) Find

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