Find the r th term in the binomial expansion. $$( z + y ) ^ { n }$$
A) $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } y ^ { r - 1 }$

B) $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } y ^ { r }$

C) $\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } y ^ { r + 1 }$

D)$\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } y ^ { r - 1 }$

E)$\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } y ^ { r - 1 }$

Question

Find the r th term in the binomial expansion. $$( z + y ) ^ { n }$$
A) $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } y ^ { r - 1 }$

B) $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } y ^ { r }$

C) $\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } y ^ { r + 1 }$

D)$\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } y ^ { r - 1 }$

E)$\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } y ^ { r - 1 }$

Quizplus · Accepted Answer

The rth term in the binomial expansion of $(z+y)^n$ is given by 
$\binom{n}{r-1}z^{n-r+1}y^{r-1}$. This can be simplified as 
$\frac{n!}{(n-r+1)!(r-1)!}z^{n-r+1}y^{r-1}$. Therefore, the correct choice is (E).

Find the R Th Term in the Binomial Expansion (z+y)n( z + y ) ^ { n }(z+y)n

Find the R Th Term in the Binomial Expansion $( z + y ) ^ { n }$