If 0- then limn- n-lim-an-bn-an-bn-

Explanation for the correct option:Finding limitn→∞lim(a^n + b^n)/(a^n b^n)0ex0ex= n→∞lim(a/b)^n+ 1/(a/b)^n 1 , a/bHence, the correct option is option (B). ...

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Standard XII

Mathematics

Limit

If 0, then li...

Question

If $0 < a < b$ , then lim_n→∞ $\lim_{n \to \infty} [\frac{(a^{n} + b^{n})}{a^{n} - b^{n}}] =$

$0$

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$- 1$

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$1$

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$D o e s n o t e x i s t$

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Solution

The correct option is B
$- 1$

Explanation for the correct option:
Finding limit
$\lim_{n \to \infty} \frac{(a^{n} + b^{n})}{(a^{n} - b^{n})} = \lim_{n \to \infty} \frac{{(\frac{a}{b})}^{n} + 1}{{(\frac{a}{b})}^{n} - 1}, \frac{a}{b} < 1 \Rightarrow {(\frac{a}{b})}^{n} = 0 = \frac{0 + 1}{0 - 1} = - 1$
Hence, the correct option is option (B).

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If 0<a<b, then limn→∞ limn→∞[(an+bn)an-bn]=

The correct option is B -1Explanation for the correct option:Finding limitlimn→∞(an+bn)(an-bn)=limn→∞(ab)n+1(ab)n-1,ab<1⇒(ab)n=0=0+10-1=-1Hence, the correct option is option (B).

If $0 < a < b$ , then lim_n→∞ $\lim_{n \to \infty} [\frac{(a^{n} + b^{n})}{a^{n} - b^{n}}] =$