Find the -1-1-12-1-22-1-1-22-1-32-1-1-20072-1-20082 - 2008

The correct option is A √((1+1/1^2+1/2^2)) = (9/4)^1/2 = 3/2 =2 1/2. √((1+1/1^2+1/2^2))+√((1+1/2^2+1/3^2))=3/2+7/6= 8/3⇒ 3 1/3 Thus, on similar lines, √((1+ ...

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Quantitative Aptitude

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Find the √1+1...

Question

Find the sum of $\sqrt{(1 + \frac{1}{1^{2}} + \frac{1}{2^{2}})} + \sqrt{(1 + \frac{1}{2^{2}} + \frac{1}{3^{2}})} + . . . . . . . . . + \sqrt{(1 + \frac{1}{2007^{2}} + \frac{1}{2008^{2}})}$ (CAT 2008)

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Solution

The correct option is A
$\sqrt{(1 + \frac{1}{1^{2}} + \frac{1}{2^{2}})} = {(\frac{9}{4})}^{\frac{1}{2}} = \frac{3}{2} = 2 - \frac{1}{2} .$

$\sqrt{(1 + \frac{1}{1^{2}} + \frac{1}{2^{2}})} + \sqrt{(1 + \frac{1}{2^{2}} + \frac{1}{3^{2}})} = \frac{3}{2} + \frac{7}{6} = \frac{8}{3} \Rightarrow 3 - \frac{1}{3}$

Thus, on similar lines,

$\sqrt{(1 + \frac{1}{1^{2}} + \frac{1}{2^{2}})} + . . . . . . \sqrt{(1 + \frac{1}{2007^{2}} + \frac{1}{2008^{2}})} = 2008 - (\frac{1}{2008})$

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Similar questions

\sqrt{1 + \frac{1}{1^{2}} + \frac{1}{2^{2}}} + \sqrt{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}}} + . . . . . + \sqrt{1 + \frac{1}{2007^{2}} + \frac{1}{2008^{2}}}

Q. If,

\sqrt{1 + \frac{1}{1^{2}} + \frac{1}{2^{2}}} + \sqrt{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}}} + \sqrt{1 + \frac{1}{3^{2}} + \frac{1}{4^{2}}} + . . . . . + \sqrt{1 + \frac{1}{(1999)^{2}} + \frac{1}{(2000)^{2}}} = x - \frac{1}{x}

, then find the value of

x

Q. Find the sum of

\sqrt{1 + \frac{1}{1^{2}} + \frac{1}{2^{2}}} + \sqrt{1 + \frac{1}{2^{2}} + \frac{1}{3^{2}}} + \sqrt{1 + \frac{1}{3^{2}} + \frac{1}{4^{2}}} + . . . . n terms

Q. If

\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + . . . . u p t o \infty = \frac{π^{2}}{6}

, then find

1 - \frac{1}{2^{2}} + \frac{1}{3^{2}} - \frac{1}{4^{2}} + . . . . u p t o \infty

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Find the sum of √(1+112+122)+√(1+122+132)+.........+√(1+120072+120082) (CAT 2008)

The correct option is A √(1+112+122)=(94)12=32=2−12. √(1+112+122)+√(1+122+132)=32+76=83⇒3−13 Thus, on similar lines, √(1+112+122)+......√(1+120072+120082)=2008−(12008)

Find the sum of $\sqrt{(1 + \frac{1}{1^{2}} + \frac{1}{2^{2}})} + \sqrt{(1 + \frac{1}{2^{2}} + \frac{1}{3^{2}})} + . . . . . . . . . + \sqrt{(1 + \frac{1}{2007^{2}} + \frac{1}{2008^{2}})}$ (CAT 2008)