Use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge to this sum? 7−14z+28z2−56z3+⋯

The series is an illustration of a geometric series.

The series is given as:

So, we have:

-- first term

--- common ratio

The sum of n terms of a geometric series is:

The number of elements in the series is 4.

So, we have:

Hence, the sum of the elements in the series is

When the sum converges, we have:

So, we have:

The sum converges at S4.

So, we have:

Cancel out common factors

Divide both sides by -1

Add 1 to both sides

Divide by 16

Take 4th roots

Rewrite as:

Hence, the variable is 0, when the sum converges at

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its 8

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.