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

Read more about geometric series at:

link

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step-by-step explanation: