Binomial theorem (H2)

TenSaru SG

Express (3+4x)^0.5 as a series of descending powers of x, up to and including the third non-zero term, simplifying the coefficient. State the set of values of x for which the series expansion is valid.

I got the expression but I don't know how to find the validity. Is it |3x^-1|<1? Anyone can help?

Thanks =)

Occam's Razor SG

|x|>3/4, i.e. x>3/4 or x<-3/4

By the way, TJC revision set A maths question?

TenSaru SG

Wow how you know?

Garrick_3658 SG

Because we are all from TJC, my dear jianliang (google rocks ok)

And you might wanna help me expose who is the intellectual one behind the Occam's Razor ign, and that avatar.

And ppl at sgf know that I won't post for such a mindless reponse, so I'll get back to topic as I intended to.

Where did I make a mistake? Isn't it:

(3+4x)^0.5 --> 3^0.5 (1+4/3x)^0.5

so valid when |4/3x| < 1 so |x| < 3/4

Blast it, since when did we ever had a chance to write validity as |x| > c ? Is this a trick of some sort?

wee_ws SG

Where did I make a mistake? Isn't it:

(3+4x)^0.5 --> 3^0.5 (1+4/3x)^0.5

so valid when |4/3x| < 1 so |x| < 3/4

Hi,

(1 + 4/3 x)^0.5 will still give terms in ascending powers of x, which is not meeting the requirement of the question.

The correct approach should instead be:

(3+4x)^0.5 = (4x)^0.5 [1 + 3/(4x)]^0.5

and the validity range is then |3/(4x)| < 1, i.e. |x| > 3/4.

Thanks!

Cheers,
Wen Shih

TenSaru SG

Because we are all from TJC, my dear jianliang (google rocks ok)

And you might wanna help me expose who is the intellectual one behind the Occam's Razor ign, and that avatar.

And ppl at sgf know that I won't post for such a mindless reponse, so I'll get back to topic as I intended to.

Where did I make a mistake? Isn't it:

(3+4x)^0.5 --> 3^0.5 (1+4/3x)^0.5

so valid when |4/3x| < 1 so |x| < 3/4

Blast it, since when did we ever had a chance to write validity as |x| > c ? Is this a trick of some sort?

Nahhhh google doesn't rock, my blog does =)

Anyway, it seems that I made a stupid mistake that 3/4 = 3 XD