Answer:
The correct answer is A. 1 -1/2 + 1/4 - 1/8 + 1/16
Step-by-step explanation:
1. Let's review the information provided to us for solving the question:Series ∑⁴n = 0 [ -1/2] ⁿ2. Let's resolve the series:For n = 0, (-1/2)⁰ = 1 (Any number raised to the power of zero, except zero, equals always to one)For n = 1, (-1/2)¹ = -1/2For n = 2, (-1/2)² = -1/2 * -1/2 = 1/4For n = 3, (-1/2)³ = -1/2 * -1/2 * -1/2 = -1/8For n = 4, (-1/2)⁴ = -1/2 * -1/2 * -1/2 * -1/2 = 1/16The correct answer is A. 1 -1/2 + 1/4 - 1/8 + 1/16
The expanded form for the provided series is 1 - 2 + 4 - 8 + 16 option (B) 1 – 2 + 4 – 8 + 16 is correct.
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The sum form of the series is:
[tex]= \rm \sum_{n=0}^4 \ -2^{-n}[/tex]
After expanding by plugging n = 0, 1, 2, 3, 4
= (-2)⁰ + (-2)¹ + (-2)² + (-2)³ + (2)⁴
= 1 - 2 + 4 - 8 + 16
Thus, the expanded form for the provided series is 1 - 2 + 4 - 8 + 16 option (B) 1 – 2 + 4 – 8 + 16 is correct.
Learn more about the sequence here:
brainly.com/question/21961097
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