Find the Sum of the Infinite Series $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$

question 309

Multiple Choice

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$

• A)undefined
• B)3
• C) \(- \frac { 3 } { 5 }\)
• D) \(\frac { 6 } { 5 }\)
• E) \(- \frac { 1 } { 1 }\)

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Definitions:

Moles

A measure of quantity in chemistry representing 6.022 x 10^23 entities of a substance.

Atm

A unit of pressure defined as exactly equal to 101,325 Pa, representing atmospheric pressure at sea level.

Temperature

A measure of the thermal energy of an object or substance, indicative of how hot or cold it is, typically measured in degrees Celsius, Fahrenheit, or Kelvin.

Helium Gas

A colorless, odorless, tasteless, non-toxic, inert, monatomic gas, the first in the noble gas group in the periodic table. Its boiling and melting points are the lowest among the elements.