lim n → ∞ a n − b n a n + b n , where a > b > 1 , is equal to

limit = lim n → ∞ 1 − ( a b ) n 1 + ( a b ) n = 1 , because 0 < a b < 1 implies ( a b ) n → 0 as n → ∞

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsAlgebraic and Rational LimitsEasy2 minPYQ_2016

MathematicsEasysingle choice

$lim_{n \to \infty} \frac{a ^{n} + b ^{n}}{a ^{n} - b ^{n}},$ where $a > b > 1,$ is equal to

Options:

Answer:

Solution:

limit $= lim_{n \to \infty} \frac{1 + ( \frac{b}{a} ) ^{n}}{1 - ( \frac{b}{a} ) ^{n}} = 1,$ because $0 < \frac{b}{a} < 1$ implies $(\frac{b}{a})^{n} \to 0$ as $n \to \infty$

Stream:BITSATSubject:MathematicsTopic:LimitsSubtopic:Algebraic and Rational Limits

⏱ 2mℹ️ Source: PYQ_2016

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