Lisa considers the number

$$
x=\frac{1}{1^{1}}+\frac{1}{2^{2}}+\cdots+\frac{1}{100^{100}} .
$$

Lisa wants to know what $x$ is when rounded to the nearest integer. Help her determine its value.
The answer is 1 . Indeed, note that

$$
x \leq 1+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots+\frac{1}{2^{100}} .
$$

By the formula for the sum of a geometric series, we see that

$$
x \leq 1+\frac{1}{2}-\frac{1}{2^{101}} \text {. }
$$

Thus $x<3 / 2$, and the closest integer to $x$ is 1 .