Question
If the sum of the coefficients of all even powers of x
in the product (1 + x + x2 + … + x2n) (1 – x + x2 – x3 + … + x2n) is 89, then find the value of n.Solution
Let (1 + x + x2 + … + x2n) (1 – x + x2 – x3 + … + x2n) = a0 + a1 + a2 + a3+ …… Put x = 1 => 2n + 1 = a0 + a1 + a2 + a3 + …… …(i) Put x = -1 => 2n + 1 = a0 – a1 + a2 – a3 + …… …..(ii) Add (i) and (ii), we get 2n + 1 = 89 Or n = 44
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