SPS SPS FM 2024 October — Question 3

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionOctober
TopicGeneralised Binomial Theorem
TypeFinding unknown constant from coefficient

3. (a) Find and simplify the first three terms in the expansion, in ascending powers of \(x\), of \(\left( 2 + \frac { 1 } { 3 } k x \right) ^ { 6 }\), where \(k\) is a constant.
(b) In the expansion of \(( 3 - 4 x ) \left( 2 + \frac { 1 } { 3 } k x \right) ^ { 6 }\), the constant term is equal to the coefficient of \(x ^ { 2 }\). Determine the exact value of \(k\), given that \(k\) is positive.
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