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Sigma(r=1)^(50)(r^2)/(r^2+(11-r)^2) is e...

`Sigma_(r=1)^(50)(r^2)/(r^2+(11-r)^2)` is equal to ______.

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Verified by Experts

The correct Answer is:
25
Let I-`sum_(r=1)^(50)r^(2)/(r^(2)+(11-r)^(2))` ….(1)
Writing the series in reverse order, we get
`I=sum_(r=1)^(50)((11-r)^(2))/(r^(2)+(11-r)^(2))` …(2)
Adding (1) and (2), we get
2I=50
`rArrI=25`
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