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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
`1/(5 + x)`
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Solution
`1/(5 + x) - 1/(5(1 + x/5)`
= `1/5(1 + x/5)^(-1)`
= `1/5{1 + x/5 + (x/5)^2 - (x/5)^3 ...}`
Hence `|x/5| < 1`
⇒ ∴ |x| < 5
= `1/5 - x/5^2 + x^2/5^3 - x^3/5^4 ...`
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