Find the (r + 1) th term in the binomial expansion. $$( x + d ) ^ { n }$$

A) $\quad \frac { n ! } { ( n - r ) ! r ! } x ^ { n - r + 1 } d ^ { r - 1 }$

B) $\quad \frac { n ! } { ( n - r ) ! r ! } x ^ { n - r } d ^ { r }$

C)$\frac { n ! } { ( n - r - 1 ) ! ( r + 1 ) ! } x ^ { n - r - 1 } d ^ { r + 1 }$

D)$\frac { n ! } { ( n - r ! ( r + 1 ) ! } x ^ { n - r - 1 } d ^ { r + 1 }$

E)
$\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } x ^ { n + r - 1 } d ^ { r + 1 }$

Question

Find the (r + 1) th term in the binomial expansion. $$( x + d ) ^ { n }$$

A) $\quad \frac { n ! } { ( n - r ) ! r ! } x ^ { n - r + 1 } d ^ { r - 1 }$

B) $\quad \frac { n ! } { ( n - r ) ! r ! } x ^ { n - r } d ^ { r }$

C)$\frac { n ! } { ( n - r - 1 ) ! ( r + 1 ) ! } x ^ { n - r - 1 } d ^ { r + 1 }$

D)$\frac { n ! } { ( n - r ! ( r + 1 ) ! } x ^ { n - r - 1 } d ^ { r + 1 }$

E)
$\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } x ^ { n + r - 1 } d ^ { r + 1 }$

Quizplus · Accepted Answer

The (r + 1)th term in the binomial expansion of $(x + d)^n$ is given by $\frac{n!}{(n-r)!r!}x^{n-r}d^r$, following the binomial theorem formula $\binom{n}{r}x^{n-r}d^r$.

Find the (R + 1) Th Term in the Binomial (x+d)n( x + d ) ^ { n }(x+d)n

Find the (R + 1) Th Term in the Binomial $( x + d ) ^ { n }$