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If .^(n)C(r-1)=36, .^(n)C(r)=84 and .^(n...

If `.^(n)C_(r-1)=36, .^(n)C_(r)=84 and .^(n)C_(r+1)=126`, find n and r.

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`(.^(n)C_(r ))/(.^(n)C_(r-1)) (n-r+1)/(r )=(84)/(36)=(7)/(3) " and" (.^(n)C_(r+1))/(.^(n)C_(r )) =(n-r)/(r+1)=(126)/(84)=(3)/(2)`
`therefore (7)/(3) r-1=n-r=(3)/(2) (r+1)`
or 14r-6=9r+9 or r=3
`therefore n=9`
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