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CAT 2005 | Question: 08

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R=$\frac{30^{65}-29^{65}}{30^{64}+29^{64}}$

We knows that $(a^{n}-b^{n})=(a-b)(a^{n-1}+a^{n-2}b+a^{n-2}b^{2}+...+b^{n-1})$

R=$=\frac{(30-29)(30^{64}+30^{63}\times29+...+29^{64})}{30^{64}+29^{64}}$

here we can see clearly

$(30^{64}+30^{63}\times29+...+29^{64}) > (30^{64}+29^{64})$

and $R> 1$

 

Hence,Option(4)$R> 1.0$.
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