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TMUA 2022 · Paper 2 · Question 2 of 20

TMUA 2022 Paper 2 Question 2

Sequences and series — Binomial expansion times a finite series. Try it first; the answer and a full worked solution are below.

TMUA 2022 · Paper 2Sequences and seriesBinomial expansion times a finite series5 options
Find the coefficient of the x5 term in the expansion of (1+x)5 × ∑i=05 xi
  1. A1
  2. B5
  3. C16
  4. D25
  5. E32
Show the answer and worked solution
answer · E
  1. A1
  2. B5
  3. C16
  4. D25
  5. E32
The second factor is 1 + x + x2 + x3 + x4 + x5, with every coefficient equal to 1. So the x5 coefficient of the product is the sum of all the coefficients of (1+x)5 from x0 to x5, that is (50) + (51) + ⋯ + (55) = 25 = 32.