Saturday, February 16, 2008

Binomial Expansion


1. (i) Calculate the coefficient of in the expansion of . [2]

(ii) Obtain the expansions of and in ascending powers of x. Hence or otherwise, find the coefficient of x, x2 and x3 in the expansion of . [4]


2. (a)

(i) Find the first three terms in the expansion, in ascending powers of x, of . [2]

(ii) Hence find the value of p such that the coefficient of in the expansion of is . [3]


(b) Find the term independent of x in the expansion of . [3]


3. Write down and simplify the first four terms in the expansion, in

ascending powers of x, of . [2]

Use this expansion to

  1. estimate the value of , correct to 3 decimal places, [2]

  2. find the coefficient of in the expansion

. [2]


    1. (a)

(i) Obtain the expansion, in ascending powers of x, of . [3]

(ii) Hence find the coefficient of in the expansion of [2]

(b) Find the term independent of x in the expansion of . [3]


  1. (a) Find the term independent of x in the expansion of . [4]


    1. Expand up to the term in x3. [ 4 ]


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