Use Substitution to Find the Taylor Series at X = $$\ln \left( \frac { 1 + x ^ { 3 } } { 1 - x ^ { 3 } } \right)$$

question 314

Multiple Choice

Use substitution to find the Taylor series at x = 0 of the given function.
- $$\ln \left( \frac { 1 + x ^ { 3 } } { 1 - x ^ { 3 } } \right)$$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 6 n + 3 } } { 6 n + 3 }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } x ^ { 3 n } } { n }\)
• C) \(2 \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 6 n + 3 } } { 2 n + 1 }\)
• D) \(2 \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 6 n + 3 } } { 6 n + 3 }\)

---

Definitions:

Autonomy

The right or condition of self-government, or in personal context, the capacity to make an informed, uncoerced decision.

Ostracism

Deliberate social exclusion of individuals or groups.

Autonomy

The state or condition of having independence or freedom, or the right to self-govern.

Affiliation

The connection or association between individuals or organizations, often formed for mutual benefit or to achieve a common goal.