To Determine a Particular Term in the Expansion
Category : JEE Main & Advanced
In the expansion of \[{{\left( {{x}^{\alpha }}\pm \frac{1}{{{x}^{\beta }}} \right)}^{n}}\], if \[{{x}^{m}}\] occurs in \[{{T}_{r+1}}\], then \[r\] is given by \[n\alpha -r(\alpha +\beta )=m\] \[\Rightarrow \] \[r=\frac{n\alpha -m}{\alpha +\beta }\]
Thus in above expansion if constant term which is independent of \[x,\] occurs in \[\frac{2n!}{(n-r)!\text{ }(n+r)!}\] then \[r\] is determined by
\[n\alpha -r(\alpha +\beta )=0\]\[\Rightarrow \]\[r=\frac{n\alpha }{\alpha +\beta }\]
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