Write as a series in ascending powers of x, as far as the term in x3 , and state the values of x for which the expansion is valid: root(4+x).

Use the binomial expansion, which, for (a + x)ⁿ = aⁿ + na^n-1x + n(n-1)a^n-2x²/2! + n(n-1)(n-2)a^n-3x³/3! + ...

 

Here: a = 4, n = 1/2 (because √(4 + x) = (4 + x)^1/2), and you don't need to go further than the terms written above because these go as far as the x³ term.

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