Maclaurin series of ln ⁡ ( 2 + x 2 )I know that ln ⁡...

Logan Wyatt

Logan Wyatt

Answered

2022-07-01

Maclaurin series of ln ( 2 + x 2 )
I know that ln ( 1 + x ) = n = 1 ( 1 ) n 1 n x n
So is ln ( 1 + x 2 ) = n = 1 ( 1 ) n 1 n x 2 n ?
I don't know what to do next then.

Answer & Explanation

Oliver Shepherd

Oliver Shepherd

Expert

2022-07-02Added 24 answers

We are looking at ln 2 + ln ( 1 + x 2 2 ) . Use the series for ln ( 1 + t ), and replace t everywhere by x 2 2

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