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Question Number 18758 by 786786AM last updated on 29/Jul/17

If the coefficient of r^(th) and (r+1)^(th) terms in the expansion of (3+7x)^(29) are equal, then r equals

Ifthecoefficientofrthand(r+1)thtermsintheexpansionof(3+7x)29areequal,thenrequals

Answered by Tinkutara last updated on 29/Jul/17

T_(r+1) =^n C_r 3^r 7^(n−r) x^(n−r) T_r =^n C_(r−1) 3^(r−1) 7^(n−r+1) Now^(29) C_r 3^r 7^(29−r) =^(29) C_(r−1) 3^(r−1) 7^(30−r) ⇒ 3^(29) C_r = 7^(29) C_(r−1) (3/7) = ((r (r − 1)! (29 − r)!)/((30 − r) (29 − r)! (r − 1)!)) 90 − 3r = 7r r = 9

Tr+1=nCr3r7n−rxn−rTr=nCr−13r−17n−r+1Now29Cr3r729−r=29Cr−13r−1730−r⇒329Cr=729Cr−137=r(r−1)!(29−r)!(30−r)(29−r)!(r−1)!90−3r=7rr=9

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