Question 730767
.
if the 21st and 22nd terms in the expansion of (1+x)^44 are equal, find the value of x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The 21th term is  C(44,20)*x^20 = {{{(44!/(20!*24!))*x^20}}}.


The 22th term is  C(44,21)*x^21 = {{{(44!/(21!*23!))^x^21}}}.


They are equal

    {{{(44!/(20!*24!))*x^20}}} = {{{(44!/(21!*23!))^x^21}}}.


It implies

    {{{(21!*23!)/(20!*24!)}}} = x,

or

    x = {{{21/24}}} = {{{7/8}}}.



<U>ANSWER</U>.  x = {{{7/8}}}.
</pre>

Solved.


-------------------------


The answer in the post by @lynnlo is incorrect.
Simply ignore his post.