GATE 2014 EC (EC4) – Question 29
$x[n]=0.5^nu[n]$ is convolved with itself to obtain y[n]. Find $\sum_{n=-\infty}^{\infty}y[n]$.
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Correct answer: 3.9 to 4.1
Explanation
The absolutely summable sequence has sumΣₙ₌₀∞(1/2)ⁿ=2. The sum of a convolution equals the product of the two sequence sums, soΣy[n]=2×2=**4**. Equivalently y[n]=(n+1)(1/2)ⁿu[n], whose series also sums to4.