Question

Given \[ x[n]=\left\{\begin{array}{cl} |n|, & -3 \leq n \leq 3 \\ 0, & \text { otherwise } \end{array}\right. \] Determine the sequence $ y[n]=\sum_{k=-\infty}^{n} x[k] $ \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline$ n $ & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline$ y[n] $ & 0 & & & & & & & & \\ \hline \end{tabular}

          Given
\[
x[n]=\left\{\begin{array}{cl}
|n|, & -3 \leq n \leq 3 \\
0, & \text { otherwise }
\end{array}\right.
\]

Determine the sequence \( y[n]=\sum_{k=-\infty}^{n} x[k] \)
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline\( n \) & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\
\hline\( y[n] \) & 0 & & & & & & & & \\
\hline
\end{tabular}

$Given x[n]={ |n|, -3 ≤ n ≤ 3 0, otherwise . Determine the sequence y[n]=∑k=-∞^n x[k] n -4 -3 -2 -1 0 1 2 3 4 y[n] 0$

Added by Carla S.

Comprehensive Mathematics for JEE Advanced

Ravi Prakash; Ajay Kumar; Usha Gupta 2019 Edition

Chapter 5

Instant Answer

Solved by Expert Aman Gupta

07/12/2021

Step 1

Given: \[ x[n] = \begin{cases} |n|, & -3 \leq n \leq 3 \\ 0, & \text{otherwise} \end{cases} \] Calculate $ x[n] $ for each $ n $ from -4 to 4: - $ x[-4] = 0 $ - $ x[-3] = 3 $ - $ x[-2] = 2 $ - $ x[-1] = 1 $ - $ x[0] = 0 $ - $ x[1] = 1 $ - Show more…

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Given \[ x[n]=\left\{\begin{array}{cl} |n|, & -3 \leq n \leq 3 \\ 0, & \text { otherwise } \end{array}\right. \] Determine the sequence $ y[n]=\sum_{k=-\infty}^{n} x[k] $ \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline$ n $ & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline$ y[n] $ & 0 & & & & & & & & \\ \hline \end{tabular}