Isaac Physics Working with Terms-HELP ME

Yh I cant do this q for some reason, i have the correct answer but it wants it in a special form.
Q:
https://isaacphysics.org/questions/binomial_series5?board=192ea231-defd-4eda-ba8f-1dffb3abccdb&stage=a_level
Just search Working with Terms Isaac Physics if u cant use the link.
I got (n-r)/(r+1) * (x^(r+1)/(2*x^r)). However, when you submit this you get this message:
This is the correct answer for the ratio of the (r+1)th power of x to the rth power of x in the expansion, however what is the power of x in the first term of the expansion?
PLease help me thanks in advance

Looks like a simple indexing problem (though your x's could be simplified).
First term is 1
Second term is nx/2
....
so just be clear about which terms the r+1th and rth terms refer to.

sorry i dont understnad what your saying - i used binomial expansion to get the first term? why is it 1. and for the second, it isnt nx/2, as it is from one to another, x, increases in quantities of 1 from one term to another

Edited - Probably best to consider the case for (1+x)^2 = 1+2x+x^2 and consider the ratio of the first to zeroth term so r=0. We know the ans is 2x/1=2x, so using your expression
(n-r)/(r+1) x = (2-0)/(1) x = 2x
so correct. They want an offset of 1 in r so it would be considering the r to the r-1 where r starts from 0 or if you assume the first term is (r=) 1, then it gives the same result. However, its not the usual definition/consistent with nCr.

so i use r-1/r ? sorry i dont underdstnad what your saying

The error message in the OP is that theyre making a distinction between the index associated with the power of x, so
1*x^0 + n*x^1 + n(n-1)/2*x^2 + ...
and the index of the term in the series expansion. The first term (r=1) has zeroth power. The second term (r=2) has power 1. The third term (r=3) has power 2, .... So the rth term in the series is
nC(r-1) x^(r-1)

Sorry I’m still confused. So the Rth term is in fact the r-1th term?

Pretty much - imho a dodgy question. So just adjust the terms of the numerator and denominator in the OP to account for an offset by 1. Not sure what youve typed in here.
Note as in #1, the x terms simplify.

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