Find the Sum of the Geometric Series for Those X $$\sum _ { n = 0 } ^ { \infty } | \sin 8 x | ^ { n }$$

question 42

Multiple Choice

Find the sum of the geometric series for those x for which the series converges.
- $$\sum _ { n = 0 } ^ { \infty } | \sin 8 x | ^ { n }$$

• A) \(\frac { 8 } { 1 + | \sin 8 x | }\)
• B) \(\frac { 1 } { 1 + | \sin 8 x | }\)
• C) \(\frac { 1 } { 1 - | \sin 8 x | }\)
• D) \(\frac { 8 } { 1 - | \sin 8 x | }\)

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Definitions:

Premise

An initial statement or proposition from which other statements are derived or reasoned out.

Conclusion

The end or final part of something, especially a period of time, an activity, or a story; in logic, it's the statement that logically follows from the premises.

Standard Form

A specific, organized way of presenting information or arguments, often used in mathematics, philosophy, and logic.

Proposition

A statement that expresses a judgement or opinion and can be either true or false.