If 1 + 4 x + 7 x 2 + 10 x 3 + ⋯ = 35/16 for ∣ x ∣ < 1 , find x .

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MathematicsSequence & SeriesA.G.P.Medium2 minQB

MathematicsMediumsingle choice

If $1 + 4 x + 7 x^{2} + 10 x^{3} + \dots = 35/16$ for $∣ x ∣ < 1$ , find $x$ .

Answer:

Solution:

The sum is $(1 + 2 x) / (1 - x)^{2}$ . Equating it to $35/16$ yields $(5 x - 1) (7 x - 19) = 0$ . Since $∣ x ∣ < 1$ , only $x = 1/5$ qualifies.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.G.P.

⏱ 2mℹ️ Source: QB

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