An infinite geometric series has first term 2 and sum S . If its common ratio is r  = 0 and ∣ S − 2∣ < 1/10 , find the interval containing r .

Convergence and S = 2/ ( 1 − r ) give ∣ S − 2∣ = ∣2 r / ( 1 − r ) ∣ − 1/19 and r < 1/21 . The stem excludes 0, giving option (D).

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MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediumsingle choice

An infinite geometric series has first term 2 and sum $S$ . If its common ratio is $r \neq = 0$ and $∣ S - 2∣ < 1/10$ , find the interval containing $r$ .

Options:

Answer:

Solution:

Convergence and $S = 2/ (1 - r)$ give $∣ S - 2∣ = ∣2 r / (1 - r) ∣ < 1/10$ . Because $r < 1$ , the two inequalities yield $r > - 1/19$ and $r < 1/21$ . The stem excludes 0, giving option (D).

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

⏱ 2mℹ️ Source: QB

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