QJEEM19Maa479: JEE Main 2019 Mathematics - Class 11 JEEM19Maa479 Solution: The sum of an infinite geometric series with positive terms is…

Question

Verified Solution • 2025–26 Session moderate

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is

\frac{27}{19}

.Then the common ratio of this series is :

Accepted Answer

\frac{a}{1 - r} = 3 . . . . . (1)

\frac{a^{3}}{1 - r^{3}} = \frac{27}{19} \Rightarrow \frac{27 {(1 - r)}^{3}}{1 - r^{3}} = \frac{27}{19}

\Rightarrow 6 r^{2} - 13 r + 6 = 0

\Rightarrow r = \frac{2}{3}

as

| r | < 1

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