1. **Problem Statement:** Given the discrete-time signal $x[n] = (n+1)\left(\frac{1}{4}\right)^n u[n]$, where $u[n]$ is the unit step function, analyze or describe the signal. 2. **Understanding the Signal:** - The term $(n+1)$ is a linear term increasing with $n$. - The term $\left(\frac{1}{4}\right)^n$ is an exponential decay since $\frac{1}{4} < 1$. - The unit step function $u[n]$ ensures the signal is zero for $n < 0$ and equals the expression for $n \geq 0$. 3. **Behavior of the Signal:** - For $n \geq 0$, $x[n]$ grows linearly by $(n+1)$ but is multiplied by an exponentially decaying factor $\left(\frac{1}{4}\right)^n$. - As $n$ increases, the exponential decay dominates, causing $x[n]$ to approach zero. 4. **Summary:** - The signal starts at $x[0] = (0+1)\left(\frac{1}{4}\right)^0 = 1$. - It initially increases slightly due to $(n+1)$ but then decays rapidly to zero because of the exponential term. - The unit step $u[n]$ restricts the signal to $n \geq 0$. This type of signal is common in discrete-time systems where a linearly weighted exponential decay is considered, often used in signal processing and system analysis.