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Solution :

Here coefficient of `T_(r ), T_(r+1)`, and `T_(r+2)` in `(1+y)^(m)` are in <br> A.P. <br> `rArr .^(m)C_(r-1), .^(m)C_(r )` and `.^(m)C_(r+1)` are in A.P. <br> `rArr 2.^(m)C_(r ) = .^(m)C_(r-1)+.^(m)C_(r+1)`. <br> or `2 = (.^(m)C_(r+1))/(.^(m)C_(r )) + (.^(m)C_(r-1))/(.^(m)C_(r )) = (r)/(m-r+1)+(m-r)/(r+1)` <br> or `2-(r)/(m-r+1)=(m-r)/(r+1)` <br> or `(2m-3r+2)/(m-r+1) = (m-r)/(r+1)` <br> or `2mr -3r^(2) +2r+2m-3r+2 = m^(2) - mr + m - mr + r^(2) - r` <br> or `m^(2)(4r+1)m + 4r^(2) - 2 = 0`