If the sum of the coefficients in the expansion of
`(1 + 2x)^(n) ` is 6561 , the greatest term in the expansion for ` x = 1//2`, is

Options

A. `4^(th)`
B. `5^(th)`
C. `6^(th)`
D. none of these

Answer

b

Explanation

Sum of the coefficients in the expansioin of
`(1 + 2x)^(n) ` is 6561
`therefore ( 1 + 2x)^(n) = 6561,` when x = 1
`rArr 3^(n) = 6561 rArr 3^(n) = 3^(8) rArr n = 8`
`because (T_(r +1))/(T_(r) )gt 1 rArr (9 -r)/(r) gt 9 - r gt r rArr 2r lt 9 rArr lt 4 (1)/(2)`
Hence, `5 ^(th)` term is the greatest term.