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10 Apr 2008 09:54:41 IST

Subject: Re:few Ds Rates awaiting...`pls........salutes assured

anchitsaini (4315)

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$1) \\ \\ \mbox{on rationalising the denominator }\\ \\ T_1 = \frac{(4 + \sqrt{3})(1 - \sqrt{3})}{-2}\\ \\ \mbox{on opening brackets we get }\\ \\ T_1 = \frac{1 - 3\sqrt{3}}{-2}\\ \\ \mbox{similarly we get }\\ \\ T_2 = \frac{3\sqrt3 - 5\sqrt{5}}{-2} \\ \\ T_3 = \frac{5\sqrt5 - 7\sqrt{7}}{-2} \\ \\ \mbox{or T_r } = \frac{(2n-1)\sqrt{2n-1} - (2n+1)\sqrt{2n+1}}{-2} \\ \\$

$\mbox{ therefore series comes something like }\\ \\ \frac{1 - 3\sqrt{3} + 3\sqrt{3} - 5\sqrt{5} ....(2n-1)\sqrt{2n+1} - (2n+1)\sqrt{2n+1}}{-2}\\ \\ \sum_{r=1}^{n}T_r= \frac{1 - (2n+1)\sqrt{2n+1}}{-2} \\ \\ \mbox{here } n = 84 \\ \\ \mbox{ hence answer is }\frac{1 - 169\sqrt{169}}{-2} = 1098$

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