If lim n → ∞ a n - 1 + n 2 1 + n = b , where a is finite number, then

lim n → ∞ an ( 1 + n ) - 1 + n 2 1 + n = lim n → ∞ ( a - 1 ) n 2 + a n - 1 n + 1 = ∞ , If a - 1 ≠ 0 limit does not exist and if a - 1 = 0 , then lim n → ∞ a n - 1 n + 1 = a = b ⇒ a = b = 1

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsGeneral ( Limit existence)Easy2 minPYQ_2017

MathematicsEasysingle choice

If $\lim_{n \to \infty} (a n - \frac{1 + n^{2}}{1 + n}) = b$ , where $a$ is finite number, then

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Answer:

Solution:

$\lim_{n \to \infty} \frac{an (1 + n) - (1 + n^{2})}{1 + n}$

$= \lim_{n \to \infty} \frac{(a - 1) n^{2} + a n - 1}{n + 1} = \infty$ ,

If $a - 1 \neq 0$ limit does not exist and if $a - 1 = 0$ , then

$\lim_{n \to \infty} \frac{a n - 1}{n + 1} = a = b$

$\Rightarrow a = b = 1$

Stream:BITSATSubject:MathematicsTopic:LimitsSubtopic:General ( Limit existence)

⏱ 2mℹ️ Source: PYQ_2017

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