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प्रश्न
Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid
`(5 + x^2)^(2/3)`
उत्तर
`(5 + x^2)^(2/3) = {5(1 +x^2/5)}^(2/3)`
= `5^(2/3) [(1 + x^2/5)^(2/3)]`
= `5^(2/3) {1 + 2/3(x^2/5) + (2/3(2/3 - 1))/(2.1) (x^2/5)^2 ...}`
= `5^(2/3) {1 + (2x^2)/15 - 2/(9 xx 2) (x^4/25) ...}`
= `5^(2/3) {1 + (2x^2)/15 - x^4/225 ...}`
Hence `|x^2/5| < 1`
⇒ |x2| < 5
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