If (2+x3)55 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the expansion are equal, then these terms are :
Coefficient of xr and xr+1 are equal.
Coefficient of Tr+1= Coefficient
of Tr+2
⇒55Cr(2)55−r(13)r=55Cr+1(2)54−r(13)r+1
.
55!(55−r)!r!(2)=55!(54−r)!(r+1)!13
⇒6(r+1)=55−r
⇒r=7
So, the terms will be 8th and 9th