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STD 11 - basic of algoritham — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - basic of algoritham4 Marks
Question
$\sum {{1 \over {1 + {x^{a - b}} + {x^{a - c}}}} = } $
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Answer

a
(a)  $\sum\limits_{}^{} {{1 \over {1 + {x^{a - b}} + {x^{a - c}}}} = \sum\limits_{}^{} {{{{x^{b + c}}} \over {{x^{b + c}} + {x^{c + a}} + {x^{a + b}}}}} } $

= ${1 \over {{x^{b + c}} + {x^{c + a}} + {x^{a + b}}}}\sum\limits_{}^{} {{x^{b + c}}} $

= ${1 \over {{x^{b + c}} + {x^{c + a}} + {x^{a + b}}}}\,({x^{b + c}} + {x^{c + a}} + {x^{a + b}}) = 1$.

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