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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

The value of _ n → ∞ 3.2 ^ n + 1 - 4.5 ^ n + 1 5.2 ^ n + 7.5 ^ n is...

The value of lim⁡n→∞3.2n+1−4.5n+15.2n+7.5n\lim_{n \to \infty} \dfrac{{3.2}^{n + 1} - {4.5}^{n + 1}}{{5.2}^{n} + {7.5}^{n}} is equal to

Options

  1. A35\dfrac{3}{5}
  2. B−47- \dfrac{4}{7}
  3. C−207- \dfrac{20}{7}
  4. D00

Correct answer

C. −207- \dfrac{20}{7}

Step-by-step solution

\lim_{n \to \infty} \dfrac{{3.2}^{n + 1} - {4.5}^{n + 1}}{{5.2}^{n} + {7.5}^{n}}<br/><br/><br /><br />= \lim_{n \to \infty}\dfrac{{5}^{n}\left(6 . {\left(\dfrac{2}{5}\right)}^{n} - 20\right)}{{5}^{n}\left(5 . {\left(\dfrac{2}{5}\right)}^{n} + 7\right)} = - \dfrac{20}{7} \left(∵ \lim_{n \to \infty} {\left(\dfrac{2}{5}\right)}^{n} = 0\right)
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