If the number of terms in the expansion of \[{\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,\] is 28, then the sum of the coefficients of all the terms in this expansion, is :
Solutions · 1
Official solution
Total no of terms in \[{\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n}\] = n+2C2 = 28
(n+2)(n+1) = 56
\[ \Rightarrow n = 6\]
Sum of coefficient = (1 - 2 + 4)6 = 36 = 729