(a) Write down the first three terms of the binomial expansion (1 + 3x in ascending powers of x.
(b) Use the expansion in (a) to find, correct to three decimal places, the value of .
Majority of the candidates were reported not to have performed well in this question. This the report attributed to the fractional power of the expression. Expanding this expression gave (1 + 3x = + 1/3(3x) + 1/3(-2/3)(3x)2 + …. = 1 + x – x2 + …. = 3(1 + 1/27 = 3[1 + - ()2 + …] = 3[1 + 0.0123457 – 0.0001524] = 3(1 + 0.0121933 …) = 3.037 to 3 decimal places.
in ascending powers of x.
.
= 
+ 1/3(3x) + 1/3(-2/3)(3x)2 + …. = 1 + x – x2 + …. 
= 3(1 + 1/27
= 3[1 + 
- (
)2 + …] = 3[1 + 0.0123457 – 0.0001524] = 3(1 + 0.0121933 …) = 3.037 to 3 decimal places.