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Question

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 :

A
7th and 8th
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B
8th and 9th
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C
28th and 29th
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D
27th and 28th
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Solution

The correct option is A 8th and 9th

Coefficient of xr and xr+1 are equal.


Coefficient of Tr+1= Coefficient of Tr+2


55Cr(2)55r(13)r=55Cr+1(2)54r(13)r+1

.
55!(55r)!r!(2)=55!(54r)!(r+1)!13


6(r+1)=55r


r=7


So, the terms will be 8th and 9th


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