Which of the following is the correct expanded form for the series below?

a. 1-1/2+1/4-1/8+1/16 b. 1-1/2-1/4-1/8-1/16 c. 0-1/2+1/4-1/8+1/16 d. 0-1/2-1/4-1/8-1/16

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] ⁿ

2. 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 = -1/2

For n = 2, (-1/2)² = -1/2 * -1/2  = 1/4

For n = 3, (-1/2)³ = -1/2 * -1/2 * -1/2 = -1/8

For n = 4, (-1/2)⁴ = -1/2 * -1/2 * -1/2 * -1/2 = 1/16

The correct answer is A. 1 -1/2 + 1/4 - 1/8 + 1/16

b is the answer that makes most sense

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places