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

Question

Quizplus · Accepted Answer

The $(r+1)$th term in the binomial expansion of $(c + d)^n$ is given by the binomial theorem as $\frac{n!}{(n-r)!r!}c^{n-r}d^r$. This matches choice B, considering the term index starts from 0, making the $(r+1)$th term correspond to $r$ in the formula.

Find The (r+1)( r + 1 )(r+1) Th Term in the Binomial Expansion

Find The $( r + 1 )$ Th Term in the Binomial Expansion