Question : If $x=-1$, then the value of $\frac{1}{x^{99}}+\frac{1}{x^{98}}+\frac{1}{x^{97}}+\frac{1}{x^{96}}+\frac{1}{x^{95}}+\frac{1}{x^{94}}+\frac{1}{x}-1$ is:
Option 1: 1
Option 2: 0
Option 3: –2
Option 4: –1
Correct Answer: –2
Solution :
We have,
$\frac{1}{x^{99}}+\frac{1}{x^{98}}+\frac{1}{x^{97}}+\frac{1}{x^{96}}+\frac{1}{x^{95}}+\frac{1}{x^{94}}+\frac{1}{x}-1$
Substituting value of $x=–1$ in the given expression,
$=\frac{1}{(–1)^{99}}+\frac{1}{(–1)^{98}}+\frac{1}{(–1)^{97}}+\frac{1}{(–1)^{96}}+\frac{1}{(–1)^{95}}+\frac{1}{(–1)^{94}}+\frac{1}{(–1)}-1$
$=-1+1-1+1-1+1-1-1$
$=–2$
Hence, the correct answer is –2.
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