The expression 22 - 1-22 - 1 - 32 - 1-32 - 1 - 42 - 1-42 - 1 - - - 20112 - 1-20112 - 1lies in the interval

The correct option is D (2011, 2011 1/2 ) We can write the expressions as #160; #160;∑ _r = 2^2011r^2 + 1/r^2 1 = ∑[1 + 2/(r + 1) (r 1)] #160 ...

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Summation by Sigma Method

The expressio...

Question

The expression
$\frac{2^{2} + 1}{2^{2} - 1} + \frac{3^{2} + 1}{3^{2} - 1} + \frac{4^{2} + 1}{4^{2} - 1} + . . . . . . . . . . . + \frac{(2011)^{2} + 1}{(2011)^{2} - 1}$
lies in the interval

(2011, 2010 \frac{1}{2})

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(2011 - \frac{1}{2011}, 2011 - \frac{1}{2012})

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(2011, 2011 \frac{1}{2})

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(2012, 2012 \frac{1}{2})

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\frac{2^{2} + 1}{2^{2} - 1} + \frac{3^{2} + 1}{3^{2} - 1} + \frac{4^{2} + 1}{4^{2} - 1} + . . . . . . . . . . + \frac{(2011)^{2} + 1}{(2011)^{2} - 1}

\frac{2^{2} + 1}{2^{2} - 1} + \frac{3^{2} + 1}{3^{2} - 1} + \frac{4^{2} + 1}{4^{2} - 1} + . . . . . + \frac{(2011)^{2} + 1}{(2011)^{2} - 1}

1 + 2 + 3 + 4 + . . . . . + n = ?

1 + 2 + 3 + 4 + . . . . . + (n - 1) = ?

1 + 1 + 1 + 1 + . . . . . + n = ?

1 + 1 + 1 + 1 + . . . . . . + (n - 1) = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + n^{2} = ?

1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . + {(n - 1)}^{2} = ?

x = \frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . .,

y = \frac{1}{1^{2}} + \frac{3}{2^{2}} + \frac{1}{3^{2}} + \frac{3}{4^{2}} + . .

z = \frac{1}{1^{2}} - \frac{1}{2^{2}} + \frac{1}{3^{2}} - \frac{1}{4^{2}} + . . . .,

\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

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