**9. The sum of the first four terms in the expansion of (1-2x)^4 is equal to the sum of the first three terms in the expansion of (1-x)^8. Show that this is true only if x=0 or x=-(1)/(8)
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ScanSolve AI Answer
9. The sum of the first four terms in the expansion of $(1-2x)^4$ is equal to the sum of the first three terms in the expansion of $(1-x)^8$. Show that this is true only if $x=0$ or $x=-\frac{1}{8}$.
Step 1: Expand $(1-2x)^4$ and find the sum of its first four terms.
Using the binomial theorem $(A+B)^n = \sum_{r=0}^{n} \binom{n}{r} A^{n-r} B^r$:
For $(1-2x)^4$, $A=1$, $B=-2x$, $n=4$.
The terms are
