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).

I don't know what this means or how to do it.

Thanks

Guest Nov 24, 2014

#1**+5 **

Use the binomial expansion, which, for (a + x)^{n} = a^{n} + na^{n-1}x + n(n-1)a^{n-2}x^{2}/2! + n(n-1)(n-2)a^{n-3}x^{3}/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 x^{3} term.

.

Alan
Nov 24, 2014

#1**+5 **

Best Answer

Use the binomial expansion, which, for (a + x)^{n} = a^{n} + na^{n-1}x + n(n-1)a^{n-2}x^{2}/2! + n(n-1)(n-2)a^{n-3}x^{3}/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 x^{3} term.

.

Alan
Nov 24, 2014