If the coefficients of r th, ( r + 1 ) th and ( r + 2 ) th terms in the binomial expansion of ( 1 + y ) m are in A.P., then m and r satisfy the equation

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Given m C , m C , m C r + 1 ​ are in A.P. ​ 2 m C r ​ = m C r − 1 ​ + m C r + 1 ​ ⇒ 2 = m C r ​ m C r − 1 ​ ​ + m C r ​ m C r + 1 ​ ​ = m − r + 1 r ​ + r + 1 m − r ​ ⇒ m 2 − m ( 4 r + 1 ) + 4 r 2 − 2 = 0 ​

Mathematics - Binomial Theorem Question with Solution | TestHub

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