The expression `(2^(2)+1)/(2^(2)-1)+(3^(2)+1)/(3^(2)-1)+(4^(2)+1)/(4^(2)-1)+........+((2011)^(2)+1)/((2011)^(2)-1)` lies in the intervalA. `(2010, 2010 1/2)`B. `(2011-1/2011,2011-1/2012)`C. `(2011,2011 1/2)`D. `(2012,2012 1/2)`

The expression `(2^(2)+1)/(2^(2)-1)+(3^(2)+1)/(3^(2)-1)+(4^(2)+1)/(4^(

1.	The expression `(2^(2)+1)/(2^(2)-1)+(3^(2)+1)/(3^(2)-1)+(4^(2)+1)/(4^(2)-1)+........+((2011)^(2)+1)/((2011)^(2)-1)` lies in the intervalA. `(2010, 2010 1/2)`B. `(2011-1/2011,2011-1/2012)`C. `(2011,2011 1/2)`D. `(2012,2012 1/2)`
Answer» Correct Answer - C `(2^(2)+1)/(2^(2)-1)+(3^(2)+1)/(3^(2)-1)+(4^(2)+1)/(4^(2)-1)+......+((2011)^(2)+1)/((2011)^(2)-1)``underset(r=2)overset(2011) sum(r^(2)+1)/(r^(2)-1)=underset(r=2)overset(2011)sum[1+2/((r+1)(r-1))]` = `underset(r=2)overset(2011) sum [1+1/(r+1)-1/(r+1)]` `=2010+[1-1/3+1/2-1/4+1/3-1/5+......+1/(2010)-1/(2012)]` =`2010+1+1/2-1/(2012)-1/(2011)` `= 2011+1/2 -[1/(2011)+1/(2012)]` lies between `(2011, 2011 1/2)`

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The expression `(2^(2)+1)/(2^(2)-1)+(3^(2)+1)/(3^(2)-1)+(4^(2)+1)/(4^(2)-1)+........+((2011)^(2)+1)/((2011)^(2)-1)` lies in the intervalA. `(2010, 2010 1/2)`B. `(2011-1/2011,2011-1/2012)`C. `(2011,2011 1/2)`D. `(2012,2012 1/2)`

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