Page 43 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Chapter 2 Sequences and Series

4
– — 1 1 1 – 1 21 – 5 2
4
1
2
Solution: (1 + x) 4 = 1 + – 4 2 x + 1·2 x + …

2
= 1 – 1 x + 5 x – …
4 32
1
3
1
1 2
4
4

1 + 1 2 – — 1 = 3 81 – —
2 80 2 80
1
—
1 2
= 3 80 4

2 81
1
2 = 3 1 5 × 2 4 2 —
4
2 3 4
= 3 · 2 (5) — 1 4
2 3
— 1
= 5 4
– — 1 1
By using the expansion of (1 + x) 4 and x = ,
80
1
1
1
5
1
1 2
1 1 + 80 2 – — = 1 – 1 1 2 + 32 80 2
4

4 80
= 1 – 1 + 1
320 40 960
= 40 833
40 960
1
— 3 40 833
4
Hence, 5 = ×
2 40 960
= 1.49535 (correct to 5 decimal places)
Exercise 2.8
3
1. Expand each of the following expressions as a series in ascending powers of x up to the term in x .
1
–2
(a) (1 + x) (b) (1 – x) –1 (c) (1 + 2x) 3
(d) (2 + x) –2 (e) (3 + 2x) –1
3
2. Expand each of the following expressions as a series in ascending powers of x up to the term in x . State
the range of values of x in each case for which the expansion is valid.
1
2
(a) 1 1 + 1 2 x 2 – — (b) (1 – 2x) — 1 3 (c) (2 + x) –1
1 x – 1
(d) (e) (1 – x) 1 + x (f)
1 + x x + 1
x + 2 1
2 –1
(g) (h) (i) (1 + x + x )
1 – 3x (x – 2)(1 + 2x)
130

02 STPM Math T T1.indd 130 3/28/18 4:21 PM