Find the Indicated Partial Sum of the Series $$\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$$

question 42

Multiple Choice

Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 4 \left( - \frac { 1 } { 2 } \right) ^ { i }$$ fourth partial sum

• A) \(\frac { 3 } { 4 }\)
• B) \(- \frac { 17 } { 12 }\) ​
• C) \(\frac { 11 } { 4 }\) ​
• D) \(\frac { 1 } { 4 }\) ​
• E) \(- \frac { 5 } { 4 }\) ​

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Definitions:

Stratosphere

The layer of the earth's atmosphere above the troposphere, characterized by a slight temperature increase and the presence of the ozone layer.

Surface Temperature

Surface temperature is the temperature near the surface of the Earth, which varies due to factors like sunlight, atmospheric conditions, and geographic location.

Ozone

A molecule composed of three oxygen atoms, found in the Earth's stratosphere, where it forms a layer that protects life by blocking most of the sun's harmful ultraviolet radiation.

Stratosphere

The second major layer of Earth's atmosphere, just above the troposphere and below the mesosphere, known for containing the ozone layer.