Question 1116575
<br>
The first term of the expansion is<br>
{{{C(44,0)*x^0 = 1*1 = 1}}}<br>
The n-th term of the expansion is<br>
{{{C(44,n-1)*x^(n-1)}}}<br>
So the 21st term is {{{C(44,20)x^20}}} and the 22nd term is {{{C(44,21)x^21}}}.<br>
We want the two terms to be equal:<br>
{{{C(44,20)x^20 = C(44,21)x^21}}}<br>
{{{x = C(44,20)/C(44,21)}}}<br>
{{{x = (44!/((20!)(24!)))/(44!/((21!)(23!)))}}}<br>
{{{x = ((21!)(23!))/((20!)(24!)) = 21/24 = 7/8}}}