Let S be the sum of the first 9 terms of the series : {x + k…} + {x² + (k + 2)…} + {x³ + (k + 4)…} + {x⁴ + (k + 6)…} + .... where a … 0 and x … 1. If S = …, then k is equal to :

Option A. S = {x + k…} + {x² + (k + 2)…} + {x³ + (k + 4)…}

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Sequences and Series

JEE Main 2020 · 2 Sep, Evening shift · Q5314

MathematicsMedium178×since 2002Q5314

Let S be the sum of the first 9 terms of the series : {x + k

a

} + {x² + (k + 2)

a

} + {x³ + (k + 4)

a

} + {x⁴ + (k + 6)

a

} + .... where a

\ne

0 and x

\ne

1. If S =

{{{x^{10}} - x + 45a\left( {x - 1} \right)} \over {x - 1}}

, then k is equal to :