JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q86

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If $\dfrac6{3^{12}}+\dfrac{10}{3^{11}}+\dfrac{20}{3^{10}}+\dfrac{40}{3^9}+\ldots+\dfrac{10240}3=2^n\cdot m$ , where m is odd, then m · n is equal to ______.

Your answer

Answer and worked solution

Official answer: 12

Sum. The first term with the GP $\frac{10\cdot2^k}{3^{11-k}}$ telescopes to $2^{12}$ .

$m=1$ , $n=12$ .

Answer: 12

Topics:Geometric progression

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JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 86