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प्रश्न
Write the first 4 terms of the logarithmic series
`log((1 - 2x)/(1 + 2x))` Find the intervals on which the expansions are valid.
उत्तर
`log((1 - 2x)/(1 + 2x))` = log(1 – 2x) – log(1 + 2x)
= `[ - 2x - (2x)^2/2 - (2x)^3/3 - (2x)^4/4 ....] - [2x- (2x)^2/2 + (2x)^3/3 - (2x)^4/4 ...]`
= `- 2x - (2x)^2/2 - (2x)^3/3 - (2x)^4/4 .... - 2x +(2x)^2/2 - (2x)^3/3+ (2x)^4/4 ...`
= `-2(2x + (2x)^3/3 + (2x)^5/5 + (2x)^7/7...)`
Hence |2x| < 1
⇒ |x| < `1/2`
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