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If r^[th] and (r+1)^[th] term in the ex...

If `r^[th]` and `(r+1)^[th]` term in the expansion of `(p+q)^n` are equal, then `[(n+1)q]/[r(p+q)]` is

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`r^(th)` term in the expansion of `(p+q)^n = n_(C_(r-1))p^(n-(r-1))q^(r-1)`
`(r+1)^(th)` term in the expansion of `(p+q)^n = n_(C_(r))p^(n-r)q^(r)`
We are given these two terms are equal.
`:. n_(C_(r-1))p^(n-(r-1))q^(r-1) = n_(C_(r))p^(n-r)q^(r)`
`=>n_(C_(r-1))p^(n-r+1)q^(r-1) = n_(C_(r))p^(n-r)q^(r)`
`=>p/q = n_(C_(r))/n_(C_(r-1)) = (n-r+1)/r->(1)`
Now, `((n+1)q)/(r(p+q))= (n+1)/(r(p/q+1)`
Putting value of `p/q` in the expression,
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