y^2 - 5y + 6
Probability
Level
pending
Determine in the set of power series R[[x]] the coefficient of y^5 in the inverse of polynomial y^2 - 5y + 6. Give your answer in 3 decimals.
The answer is 0.014.
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1 solution
y 2 − 5 y + 6 1 = y − 2 1 x y − 3 1 = y − 2 A + y − 3 B = ( y − 2 ) ( y − 3 ) A ( y − 3 ) + B ( y − 2 ) . Thus A + B = 0, -3A - 2B = 1 or A = -1, B = 1. y − 2 − 1 + y − 3 1 = 2 1 x 1 − y / 2 1 - 3 1 x 1 − y / 3 1 = [(2^-1) - (3^-1)] x y^0 + [(2^-2) - (3^-2)] x y^1 + . . . + [(2^-6) - (3^-6)] x y^5 + . . .. And [(2^-6) - (3^-6)] = .014.