Questions: 1/x + 1/x^2 + 1/x^3

Solution Steps

To evaluate the expression \(\frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}\) for a given value of \(x\), we need to compute each term separately and then sum them up. This involves calculating the reciprocal of \(x\), the reciprocal of \(x^2\), and the reciprocal of \(x^3\), and then adding these values together.

To evaluate the expression \(\frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}\) for \(x = 2\), we first calculate each term separately:

• The first term is \(\frac{1}{x} = \frac{1}{2} = 0.5\).
• The second term is \(\frac{1}{x^2} = \frac{1}{2^2} = \frac{1}{4} = 0.25\).
• The third term is \(\frac{1}{x^3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\).

Next, we sum the calculated terms: \[ 0.5 + 0.25 + 0.125 = 0.875 \]

Final Answer