Solve the Problem $\ln ( 1 + x )$ , Obtain a Series For

question 128

Multiple Choice

Solve the problem.
-Using the Maclaurin series for $\ln ( 1 + x )$ , obtain a series for $\frac { \ln \left( 1 + x ^ { 2 } \right) } { x }$ .

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

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