This document contains two mathematics quizzes covering sequences and series. Quiz 1 has three problems: (1) expressing a fraction in partial fractions and finding the expansion and convergence of a series, (2) using the method of differences to find sums of series, (3) expressing a recurring decimal as a rational number. Quiz 2 has three problems: (1) finding terms in a binomial expansion, (2) expanding a binomial expression and stating the valid range, (3) proving an equality for small x and using it to evaluate an expression.

1. Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 1 : Chapter 3 Sequences & Series
1
1. ( i ) Express in partial fraction
r ( r + 1)
n 1
( ii ) Find an expansion for ∑ and state whether or not the series is convergent. [ 6 marks ]
r =1 r ( r + 1)
2 1 1
2. ( i ) Given that = − , by using the method of differences, show that
x( x + 2) x x + 2
n 1 3 2n + 3 ∞ 1
∑ = − and determine ∑ .
x =1 x ( x + 2) 4 2(n + 1)( n + 2) x =1 x ( x + 2)
1 1 1 1
( ii) Find the sum of the series + + + ... + [8
1× 3 2 × 4 3 × 5 9 × 11
marks ]
&&
3. Express the recurring decimal 0.236 as a rational number in its lowest form. [ 4 marks ]
Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 1 : Chapter 3 Sequences & Series
1
1. ( i ) Express in partial fraction
r ( r + 1)
n 1
( ii ) Find an expansion for ∑ and state whether or not the series is convergent. [ 6 marks ]
r =1 r ( r + 1)
2 1 1
2. ( i ) Given that = − , by using the method of differences, show that
x( x + 2) x x + 2
n 1 3 2n + 3 ∞ 1
∑ = − and determine ∑ .
x =1 x ( x + 2) 4 2(n + 1)( n + 2) x =1 x ( x + 2)
1 1 1 1
( ii) Find the sum of the series + + + ... + [8
1× 3 2 × 4 3 × 5 9 × 11
marks ]
&&
3. Express the recurring decimal 0.236 as a rational number in its lowest form. [ 4 marks ]
Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 1 : Chapter 3 Sequences & Series
1
1. ( i ) Express in partial fraction
r ( r + 1)
n 1
( ii ) Find an expansion for ∑ and state whether or not the series is convergent. [ 6 marks ]
r =1 r ( r + 1)
2 1 1
2. ( i ) Given that = − , by using the method of differences, show that
x( x + 2) x x + 2
n 1 3 2n + 3 ∞ 1
∑ = − and determine ∑ .
x =1 x ( x + 2) 4 2(n + 1)( n + 2) x =1 x ( x + 2)

2. 1 1 1 1
( ii) Find the sum of the series + + + ... + [8
1× 3 2 × 4 3 × 5 9 × 11
marks ]
&&
3. Express the recurring decimal 0.236 as a rational number in its lowest form. [ 4 marks ]
Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 2 : Chapter 3 Sequences & Series
10
 1
1. In the binomial expansion of  3x +  , find
 x
( i ) the fourth term
( ii ) the term independent of x [5
marks ]
1 + x + x2
1 in ascending power of x up to and including the term in x .
2
2. ( i ) Expand
(1 + 2 x) 2
( ii) State the set of values of x for which this expansion is valid. [ 6 marks ]
3. Prove that, if x is so small that terms in x 3 and higher powers may be neglected, then
1+ x 1 1 384
= 1 + x + x 2 + ... By putting x = , show that 7= [ 7 marks ]
1− x 2 8 145
Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 2 : Chapter 3 Sequences & Series
10
 1
1. In the binomial expansion of  3x +  , find
 x
( i ) the fourth term
( ii ) the term independent of x [5
marks ]
1 + x + x2
1 in ascending power of x up to and including the term in x .
2
2. ( i ) Expand
(1 + 2 x) 2
( ii) State the set of values of x for which this expansion is valid. [ 6 marks ]
3. Prove that, if x is so small that terms in x 3 and higher powers may be neglected, then
1+ x 1 1 384
= 1 + x + x 2 + ... By putting x = , show that 7= [ 7 marks ]
1− x 2 8 145
Mathematics T STPM PAPER 1 ( 30 minutes )
Quiz 2 : Chapter 3 Sequences & Series
10
 1
1. In the binomial expansion of  3x +  , find
 x
( i ) the fourth term
( ii ) the term independent of x [5
marks ]
1 + x + x2
1 in ascending power of x up to and including the term in x .
2
2. ( i ) Expand
(1 + 2 x) 2

3. ( ii) State the set of values of x for which this expansion is valid. [ 6 marks ]
3. Prove that, if x is so small that terms in x 3 and higher powers may be neglected, then
1+ x 1 1 384
= 1 + x + x 2 + ... By putting x = , show that 7= [ 7 marks ]
1− x 2 8 145