Expand $$\((1+3 x)^{\frac{2}{3}}\)$$ in ascending powers of $$\(x\)$$, up to and including the term in $$\(x^{3}\)$$, simplifying the coefficients. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s21_qp_33 Year：2021 Question No：1
Answer:
State correct first two terms \(1+2 x\)
State a correct unsimplified version of the \(x^{2}\) or \(x^{3}\) term
Obtain the next term \(-x^{2}\)
Obtain the final term \(\frac{4}{3} x^{3}\)
State a correct unsimplified version of the \(x^{2}\) or \(x^{3}\) term
Obtain the next term \(-x^{2}\)
Obtain the final term \(\frac{4}{3} x^{3}\)
Knowledge points:
3.1.5 use the expansion of , where n is a rational number and |x| < 1. (Finding the general term in an expansion is not included.) (Adapting the standard series to expand e.g. is included, and determining the set of values of x for which the expansion is valid in such cases is also included.)
Solution:
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