If (1−2x+3x^2 )^(10) =a_0 +a_1 x+a_2 x^2 +...+a_(20) x^(20) find the value of a_1 +a_2 +...+a


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Question Number 116595 by ZiYangLee last updated on 05/Oct/20

$If {(1 - 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{20} x^{20}$ $find the value of a_{1} + a_{2} + . . . + a_{20}$
	Answered by mr W last updated on 05/Oct/20

	$p u t x = 0 :$ ${(1 - 0 + 0)}^{10} = a_{0} + a_{1} 0 + a_{2} 0 + . . . + a_{20} 0$ $\Rightarrow a_{0} = 1$ $p u t x = 1 :$ ${(1 - 2 + 3)}^{10} = a_{0} + a_{1} 1 + a_{2} 1 + . . . + a_{20} 1$ $\Rightarrow 2^{10} = a_{0} + a_{1} + a_{2} + . . . + a_{20}$ $\Rightarrow a_{1} + a_{2} + . . . + a_{20} = 2^{10} - a_{0} = 2^{10} - 1$
	Commented by ZiYangLee last updated on 05/Oct/20

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