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Question
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`2/(3 + 4x)^2`
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Solution
`2/(3 + 4x)^2 = 2/[3(1 + 4/3 x)]^2`
= `2/(9(1 + 4/3 x)^2`
= `2/9(1 + 4/3 x)^(- 2)`
= `2/9[1 - 2(4/3 x) + 3(4/3 x)^2 ...]`
= `2/9[1 - 8/3 x + 16/9 x^2]`
Hence `|(4x)/3| < 1`
⇒ ∴ |x| < `3/4`
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