Question
If $n$ is a positive integer and $(1+x)^{n}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots a_{n} x^{n}$, the value of $a_{0}-a_{2}+a_{4}-a_{6} \ldots . .-a_{102}$(a) 0(b) 1(c) $-1$(d) 2$\sqrt{2}$
Step 1
Step 1: Substitute $x=i$ in the given equation, we get \[(1+i)^{n}=a_{0}+a_{1}i+a_{2}i^{2}+\ldots a_{n}i^{n}\] Since $i^{2}=-1$, this expression can be written as \[a_{0}-a_{2}+a_{4}-a_{6}+\ldots = (1+i)^{n}\] Show more…
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