SOLUTION: In the expansion of (1+x)^21,the coefficient of (2r+1)th term is equal to the coefficient of (3r+2)th term, then find the value of r.

Question 1089122: In the expansion of (1+x)^21,the coefficient of (2r+1)th term is equal to the coefficient of (3r+2)th term, then find the value of r.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The expansion of a binomial has terms.
They are of the form with a combinatorial coefficient ,
and positive integers and such that .
There's is a certain symmetry to the combinatorial coefficients:
The first and last ones (the number and coefficients are 1;
the number and coefficients are ;
the number and coefficients are ,
and so on, so that the number and coefficients will be the same if .
So, in this case,
,
,
,
and .

Verification:

The 9th coefficient is
.
The 14th coefficient is
.
RELATED QUESTIONS
If the coefficients of (m+1)th term and the (m+3)th term in the expansion of (1+x)^20 are (answered by Edwin McCravy)

Expand (1/2-2x)^5 up to the term in x^3. If the coefficient of x^2 in the expansion of... (answered by greenestamps)

Find the coefficient of the fourth term in ascending powers of x in the expansion of (1... (answered by richwmiller)

In the expansion of (2x+1)^n, the coefficient of the x^2 term is 40n , where n is a... (answered by ikleyn)

Find the coefficient of the x^8 term in the expansion of (x + 3)^17 (answered by MathLover1)

Find the coefficient of the {{{ x^8 }}} term in the expansion of {{{ (x+3)^17... (answered by Boreal)

In the expansion of (x + 4y)^12, the numerical coefficient of the 5th term... (answered by MathLover1)

1. Find the coefficient a of the term in the expansion of the binomial. Binomial:... (answered by stanbon)

find the nth term of an A.P. whose (r+1)th term is... (answered by stanbon)