Sequence and Series
Geometric Series Sum
JEE Main 2020
Grade 11
Question:
If $2^{10} + 2^9 \cdot 3^1 + 2^8 \cdot 3^2 + \dots + 2 \cdot 3^9 + 3^{10} = S - 2^{11}$, then $S$ equals:
(1) $2^{11} + 3^{11}$
(2) $3^{11}$
(3) $\frac{3^{11} - 2^{11}}{2}$
(4) $3^{11} + 2^{11}$
Step-by-Step Solution
Key Concept: The left side is a G.P. with first term $2^{10}$, common ratio $3/2$, and 11 terms. Sum it using the GP formula and simplify.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)