If the number of terms in the expansion of (1-2x+4x^2)^n, x0, is 28, then the sum of the c…

Question

If the number of terms in the expansion of $\left(1-\dfrac2x+\dfrac4{x^2}ight)^n$, $x
e0$, is 28, then the sum of the coefficients of all the terms in this expansion, is:

Accepted Answer

Number of terms in $(a+b+c)^n$ is $\binom{n+2}{2}=28\Rightarrow(n+2)(n+1)=56\Rightarrow n=6$

Sum of coefficients: set $x=1$: $(1-2+4)^6=3^6=729$

Solutions · 1