The energy for the signal— x(n) = 3(0.5)2n n ≥ 0 will

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The energy for the signal—
x(n) = 3(0.5)²ⁿ n ≥ 0 will be—

1. 8 joules
2. 12 joules
3. 24 joules
4. None of these

Correct Option: B

E =	_{N – 1}	\|x(n)\|²
	∑
	^{n = 0}

=	_∞	\|3(0.5)²ⁿ\|²
	∑
	^{n = 0}

= 9	_∞	\|3(.5)²\|ⁿ
	∑
	^{n = 0}

= 9	_∞	(.25)ⁿ
	∑
	^{n = 0}

= 9[1 + (.25) + (.25)² + (.25)³ + … ∞]

= 9·	1
	1 – .25

= 9·	1	= 12
	1 – .75

Hence alternative (B) is the correct choice.