Write down the first three terms of the binomial expansion of $\frac{1}{2+x}$, in ascending powers

Question

Write down the first three terms of the binomial expansion of $\frac{1}{2+x}$, in ascending powers of $x$. State the values of $x$ for which the expansion is valid.

Accepted Answer

$\dfrac1{2+x}=\dfrac12-\dfrac x4+\dfrac{x^2}8+\cdots,\quad |x|<2$.

Example involving Binomial Series

Example involving Binomial Series

Solution:

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