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# For some positive integer n, the expansion of (1-x)^n has three consecutive coefficients a, b, and c that satisfy 1:7:35 What must n be?

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For some positive integer n, the expansion of (1-x)^n has three consecutive coefficients a, b, and c that satisfy 1:7:35 What must n be?

Aug 11, 2021

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For some positive integer n, the expansion of (1-x)^n has three consecutive coefficients a, b, and c that satisfy 1:7:35 What must n be?

Hello Guest!

$$\large n=7$$

$$(1-x)^{\color{blue}7}={\color{blue}1}\cdot (-x^7)+{\color{blue}7}x^6+{\color{blue}35}x^4-21x^5-35x^3+21x^2-7x+1$$

!

Aug 11, 2021