3. Let $n$ be a given positive integer, and the set
$$
M=\left\{\frac{1}{2^{n}}, \frac{1}{2^{n+1}}, \cdots, \frac{1}{2^{2 n}}\right\} \text {. }
$$

Let the subsets of $M$ be denoted as $M_{1}, M_{2}, \cdots, M_{i}$. For $1 \leqslant i \leqslant t$, let $S\left(M_{i}\right)$ represent the sum of all elements in the set $M_{i}$, with the convention that $S(\varnothing)=0$. Then
$$
S\left(M_{1}\right)+S\left(M_{2}\right)+\cdots+S\left(M_{t}\right)=
$$
$\qquad$
$3.2-\frac{1}{2^{n}}$.
For any element $a$ in set $M$, since there are $2^{n}$ subsets containing $a$, each element appears $2^{n}$ times in the "sum".
$$
\begin{array}{l}
\text { Therefore, } S\left(M_{1}\right)+S\left(M_{2}\right)+\cdots+S\left(M_{t}\right) \\
=2^{n} S(M)=2^{n}\left(\frac{1}{2^{n-1}}-\frac{1}{2^{2 n}}\right)=2-\frac{1}{2^{n}} \text {. }
\end{array}
$$