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?

Solution(By Examveda Team)

$$\frac{1}{{{x^{99}}}}{\text{ + }}\frac{1}{{{x^{98}}}} + \frac{1}{{{x^{97}}}} + \frac{1}{{{x^{96}}}} + \frac{1}{{{x^{95}}}} + \frac{1}{{{x^{94}}}} + \frac{1}{x} - 1$$
  $$ = \frac{1}{{{{\left( { - 1} \right)}^{99}}}}{\text{ + }}\frac{1}{{{{\left( { - 1} \right)}^{98}}}} + \frac{1}{{{{\left( { - 1} \right)}^{97}}}} + \frac{1}{{{{\left( { - 1} \right)}^{96}}}} + $$         $$\frac{1}{{{{\left( { - 1} \right)}^{95}}}} + $$   $$\frac{1}{{{{\left( { - 1} \right)}^{94}}}} + $$   $$\frac{1}{{\left( { - 1} \right)}} - $$   $$1$$
$$\eqalign{ & = - 1 + 1 - 1 + 1 - 1 + 1 + \frac{1}{{ - 1}} - 1 \cr & = - 2 \cr} $$