Binomial theorem query (1 Viewer)

[apollo1]

Show that there will always be a term independent of x in the expansion of:

(n is a positive integer), and find that term.

 

[apollo1]

I got 3nCn

 

[apollo1]

ok so this is wat i did:

then i simplified to get:

therefore since n greater than or equal to r, a term independent of x must always exist.
3n-3r = 0
therefore 3n = 3r
therefore r = n

thefore term is 3nCn. can sumone plz confirm if my working is correct.

 

[hayabusaboston]

correct

 

[OldMathsGuy]

You want the indices to balance out, ie r = 2n therefore the term is 3nC2n.

This is the same as 3nCn (just with the indices swapped around). r = n or r = 2n are both valid solutions, and so 3nCn and 3nC2n are identical terms.

Best Regards
Old Maths Guy

 

[taeyang]

I don't even know if it wants an integer for the term ^^ but is it 3nCn ?

 

[apollo1]

You want the indices to balance out, ie r = 2n therefore the term is 3nC2n.

This is the same as 3nCn (just with the indices swapped around). r = n or r = 2n are both valid solutions, and so 3nCn and 3nC2n are identical terms.

Best Regards
Old Maths Guy

lol i luv how u do that thing at the end of your posts. very classy.