Find the r th term in the binomial expansion. $$( z + d ) ^ { n }$$
A) $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } d ^ { r }$
B) $\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } d ^ { r + 1 }$
C) $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } d ^ { r - 1 }$
D) $\quad \frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } d ^ { r - 1 }$
E) $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } d ^ { r - 1 }$

Question

Quizplus · Accepted Answer

The rth term in the binomial expansion of $(z+d)^n$ is given by the term with coefficient $\binom{n}{r-1}$, which is equivalent to $\dfrac{n!}{(n-r+1)!(r-1)!}$, multiplied by $z^{n-r+1}$ and $d^{r-1}$. Therefore, the answer is $\dfrac{n!}{(n-r+1)!(r-1)!}z^{n-r+1}d^{r-1}$, which is choice E.

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

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