H2 Binomial theorem

iamapebble SG

Hihi all, just a short question that I need help in.

See the range of values for which (1+x)^-1 is valued for |x| < 1 right? Which means if we have an expression (1+2x)^-1, the values valid are |2x|<1 -> |x| < 1/2 right? However, what if I have (1+2x^2)^(3/2) instead?

Kindly enlighten me, thank you! :D

wee_ws SG

Hi,

We will have |2x^2| < 1.

In general, |second term| < 1so that the series converge.

Thanks!

Cheers,
Wen Shih

iamapebble SG

Ahhh, I see, which means the power doesn't make a difference? :D Thanks!

eagle SG

As long as you expand in a way such that the terms are infinite, then you have to consider it...

which means the power cannot be a positive integer ;)