OpenStudy (anonymous):

Find the term that contains x^5/3 in the expansion ( x^(-2/3) + x^1/3 )^20

6 years ago
OpenStudy (yuki):

You will use the binomial theorem

6 years ago
OpenStudy (anonymous):

can u try it for me, Yuki.

6 years ago
OpenStudy (yuki):

The formula tells you, (a+b)^n = a^n + n*a^(n-1)b + nC2*a^(n-2)*b^2 ...

6 years ago
OpenStudy (yuki):

So you need to find which term makes it x^5/3

6 years ago
OpenStudy (yuki):

If you cannot see it right away, you can use this equation

6 years ago
OpenStudy (yuki):

\[{-2 \over 3}n + {1 \over 3}(20 - n ) = {5 \over 3}\]

6 years ago
OpenStudy (anonymous):

is it the 5th term ?

6 years ago
OpenStudy (yuki):

yep

6 years ago
OpenStudy (yuki):

so the fifth term of the binomial sequence is

6 years ago
OpenStudy (yuki):

\[\left(\begin{matrix}20 \\ 5\end{matrix}\right) a^5b^{15}\]

6 years ago
OpenStudy (yuki):

just substitute a and b with your binomial and the coefficient should be your answer

6 years ago