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Maths-

General

Easy

Question

If $x equals 1 plus 3 a plus 6 a squared plus 10 a cubed plus midline horizontal ellipsis.$ to $straight infinity$ terms, $vertical line a vertical line less than 1 comma y equals 1 plus 4 a plus 10 a squared plus 20 a cubed plus midline horizontal ellipsis$ $straight infinity$ terms, $vertical line a vertical line less than 1$ , then $x colon y$

$1 - a : 1$
$1 : (1 - a)$
$(1 + a) : 1$
$1: (1 + a)$

The correct answer is: $1 minus a colon 1$

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The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

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