Find the Sum of the Series $$\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 2 ^ { n } } - \frac { ( - 1 ) ^ { n } } { 2 ^ { n } } \right)$$

question 446

Multiple Choice

Find the sum of the series.
- $$\sum _ { n = 0 } ^ { \infty } \left( \frac { 1 } { 2 ^ { n } } - \frac { ( - 1 ) ^ { n } } { 2 ^ { n } } \right)$$

• A) \(\frac { 2 } { 5 }\)
• B) \(\frac { 4 } { 5 }\)
• C) \(\frac { 2 } { 3 }\)
• D) \(\frac { 4 } { 3 }\)

---

Definitions:

Internal Rate

Commonly denotes the internal rate of return (IRR), the discount rate at which the net present value (NPV) of all cash flows from a specific project is zero.

Cash Operating

The process dealing with the direct cash flows from business operations, emphasizing a company's liquidity in the short term.

Required Rate

The minimum expected return by investors to compensate for the risk of an investment, often used in capital budgeting.

Useful Life

The estimated period over which a fixed asset is expected to be usable by an organization, impacting its depreciation calculations.