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tmua.me Extreme Set C Paper 1 · Q7

Paper 1Algebra

For r=0,1,…,49r=0,1,\ldots,49, let ara_r be the coefficient of xrx^r in

(1+x)47(1−x)2.(1+x)^{47}(1-x)^2.

These coefficients satisfy the identity

ar=(49r)(r−21)(r−28)588.a_r=\binom{49}{r}\frac{(r-21)(r-28)}{588}.

What is the value of

∣a0∣+∣a1∣+⋯+∣a49∣(4721) ?\frac{|a_0|+|a_1|+\cdots+|a_{49}|}{\binom{47}{21}}\,?
A00
B49\dfrac49
C89\dfrac89
D11
E169\dfrac{16}{9}
F29\dfrac29

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