6. \[ \begin{array}{l} a_{1}=1 \\ a_{2}=1+2 \\ a_{3}=1+2+3+4 \\ a_{4}=1+2+3+4+\cdots+7+8 \\ \quad \vdots \\ a_{n}=1+2+3+4+\cdots+2^{n=-1} \end{array} \] 인 수열 $\left\{a_{\ldots}\right]$ 에 매하여 $\sum_{z=1}^{\pi} a_{z}$ 의 값은? (단. \[ 2^{18}=8102 \text { 이다.) } \] 2754 (9) $2 \pi 74$ Q 2794 (9) 2614 (5) 2834

Step 1 ：First, let's find the value of \(\pi\). We know that \(2^\pi > 8102\).

Step 2 ：\(\pi = 13\)

Step 3 ：Now that we know the value of \(\pi\), we can calculate the sum of the first \(2^{(n-1)}\) natural numbers for each \(n\) in the range \([1, \pi]\). Then, we can find the sum of these values.

Step 4 ：\(\pi = 13\)

Step 5 ：\(\sum_{z=1}^{\pi} a_{z} = 11188906\)

Step 6 ：\(\boxed{11188906}\)