Write down and simplify the first three terms, in ascending power of $x$, in the Extended Binomial

Question

Write down and simplify the first three terms, in ascending power of $x$, in the Extended Binomial expansion of $\sqrt{1+x}$. State the values of $x$ for which the expansion is valid.

Accepted Answer

$\sqrt{1+x}=1+\dfrac{x}{2}-\dfrac{x^2}{8}+\cdots$, with the standard binomial condition $|x|<1$.

Example involving Binomial Series

Example involving Binomial Series

Solution:

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