If the number of terms in the expansion of `(1-2/x+4/(x^(2))) x ne 0`, is `28`, then the sum of coefficient of all the terms in this expansion, is

Options

A. 64
B. 2187
C. 243
D. 729

Answer

d

Explanation

We know that the expansion of `(x_(1) + x_(2) +… + x_(r))^(n)`
has `""^(n + 3-1)C_(r-1)` terms . So, the expansion of `(1 - (2)/(x) + (4)/(x^(2)))^(n)` has
`""^(n + 3-1)C_(r-1)= ""^(n+2)C_(2)` terms .
` therefore ""^( n+2)C_(2)= 28 rArr (n+2) (n+1) = 8xx7 rArr n+6`
The sum of the coefficients of all terms in the expansion
of `(1 - (2)/(x) + (4)/(x^(2)))^(n)` is
`(1 - 2 + 4 )^(n) = 3^(n) = 3^(6) = 729` [Repplacing x by 1] .