Sequence and Series
Infinite Geometric Series
JEE Main 2019
Grade 11
Question:
The sum of an infinite G.P. with positive terms is $3$ and the sum of cubes of its terms is $\frac{27}{19}$. The common ratio is:
(1) $\frac{1}{9}$
(2) $\frac{1}{3}$
(3) $\frac{2}{3}$
(4) $\frac{4}{9}$
Step-by-Step Solution
Key Concept: $a/(1 - r) = 3$ and $a^3/(1 - r^3) = 27/19$. Divide the second by the cube of the first to get an equation in $r$ alone.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)