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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{n \rightarrow \infty}\left(2^n+5^n\right)^{\frac{1}{n}}$ is equal to
  • A
    2
  • ✓
    5
  • C
    e
  • D
    $\frac{1}{2}$
✓

Answer

Correct option: B.
5
B)
$\lim _{n \rightarrow \infty}\left(2^n+5^n\right)^{\frac{1}{n}}=\lim _{n \rightarrow \infty} 5\left\{1+\left(\frac{2}{5}\right)^n\right\}^{\frac{1}{n}}=5$
Alternate method:
Here, $0<2<5$
If $0 < x < y$, then $\lim _{n \rightarrow \infty}\left(x^n+y^n\right)^{1 / n}=y$
$\therefore \lim _{n \rightarrow \infty}\left(2^n+5^n\right)^{\frac{1}{n}}=5 $

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