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-20-

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} + \dots + a_{20} x^{20}

find the value of a_{1} + a_{2} + \dots + 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 + \dots + a_{20} 0

\Rightarrow a_{0} = 1

p u t x = 1 :

{(1 - 2 + 3)}^{10} = a_{0} + a_{1} 1 + a_{2} 1 + \dots + a_{20} 1

\Rightarrow 2^{10} = a_{0} + a_{1} + a_{2} + \dots + a_{20}

\Rightarrow a_{1} + a_{2} + \dots + a_{20} = 2^{10} - a_{0} = 2^{10} - 1

Commented by ZiYangLee last updated on 05/Oct/20

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