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Question
Write the first 4 terms of the logarithmic series
log(1 – 2x) Find the intervals on which the expansions are valid.
Solution
log(1 – 2x) = `- 2x - (2x)^2/2 - (2x)^3/3 - (2x)^4/4 ...`
= `- 2x - (4x^2)/2 - (8x^3)/3 - (16x^4)/4 ...`
= `2x - x^2 - (8x^3)/3 - 4x^4`
Hence |2x| < 1
⇒ |x| < `1/2`
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