I have been doing some questions on Binomial Series expansion and have been stuck on this particular question for a long time and desperately need some guidance.(adsbygoogle = window.adsbygoogle || []).push({});

Q) Expand (1/(sqrt(1-b^2(sin^2)x)))), where b = sin(1/2(theta)) as a binomial series.

Here is what I have done so far...

Let x = (b^2(sin^2)x) because I want the expression in binomial form.

So it becomes 1/sqrt(1 - x) with k = -1/2

(1-x)^-1/2 can be written in binomial form... (S is capital sigma)

= S(-1/2 n)(-x)^n

= 1 + (-1/2)(-x) + ((-1/2)(-3/2)/2!)*(-x)^2 + ...

= 1 + 1/2x - 3/8x^2 + ...

= 1 + 1/2k^2sin^2x - 3/8k^4sin^4x + ...

Any help on this question would be excellent!

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# Binomial Series

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