Page 44 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Chapter 2 Sequences and Series
4
4
3. Use the expansion of (x + y) to evaluate (1.03) , correct to four decimal places.
5
5
4. Use the expansion of (2 – x) to evaluate (1.98) , correct to five decimal places.
15
3
5. Obtain the expansion of (1 + 2x) in ascending powers of x up to the term in x . Hence, evaluate (1.002) ,
15
correct to five decimal places.
– — 1
2
6. Find the first four non-zero terms of the expansion of (1 + 2x ) 2 in ascending powers of x.
1
– —
7. Obtain the first four terms of the expansion of (1 – x) 2 in ascending powers of x. Deduce the value of
0.9, correct to four decimal places.
1
—
8. By substituting x = 0.08 into (1 + x) and its expansion, find 3 , correct to four significant figures. 2
2
2
9. By substituting x = 1 into (1 – x) – — 1 and its expansion, find 10 , correct to five significant figures.
10
–2
10. Expand (2 – x) as a series in ascending powers of x, up to the term in x .
4
Deduce the value of 1 , correct to three significant figures.
(1.8) 2
— 1 1
2
11. Expand (1 + 2x) in ascending powers of x, up to the term in x . By substituting x = , find an
3
approximation for 5 , giving your answer correct to three decimal places. 8
3
12. Expand 1 – 3x in ascending powers of x, up to the term in x . State the range of values of x for which
1 + 4x
the expansion is valid.
2 5
13. Expand (1 – x – 2x ) in ascending powers of x, up to the term in x . By substituting
4
5
x = 0.01, estimate the value of (0.9898) , correct to six decimal places.

Summary

1. A series S = u + u + u + … + u is said to be convergent if there exists a finite number a, such that
1
n
n
3
2
lim S = a.
n → ∞ n
A series is said to be divergent if it is not convergent.
2. Sum of the first n positive integers is
n 1
∑ r = n(n + 1)
r = 1 2
Sum of the squares of the first n positive integers is
n
2
∑ r = 1 n(n + 1)(2n + 1)
r = 1 6
Sum of the cubes of the first n positive integers is
n 1
2
3
∑ r = n (n + 1) 2
r = 1 4
th
3. For an arithmetic progression with first term a and common difference d, the n term is u = a + (n – 1) d.
n
Sum of the first n terms is
S = n [2a + (n – 1)d]
2
n
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02 STPM Math T T1.indd 131 3/28/18 4:21 PM