Find the 5th term in the binomial expansion. $$( c - t ) ^ { n }$$
A) $\frac { n ! } { ( n - 4 ) ! 4 ! } c ^ { n - 4 } t ^ { 4 }$
B) $\quad \frac { ( n - 4 ) ! } { ( n - 4 ) ! 4 ! } c ^ { n - 4 } t ^ { 4 }$
C) $\quad \frac { n ! } { ( n - 5 ) ! 5 ! } c ^ { n - 5 } t ^ { n }$
D) $\frac { n ! } { ( n - 4 ) ! } c ^ { n - 4 } t ^ { 4 }$
E) $\frac { n ! } { ( n - 5 ) ! 5 ! } c ^ { n - 5 } t ^ { 5 }$

Question

Quizplus · Accepted Answer

The 5th term in the binomial expansion $(c - t)^n$ can be found using the formula for the $k$th term: $\binom{n}{k}c^{n-k}t^k$, where $k = 4$ for the 5th term. Simplifying, we get $\frac{n!}{(n-4)!4!}c^{n-4}t^4$, which matches option A.

Find the 5th Term in the Binomial Expansion (c−t)n( c - t ) ^ { n }(c−t)n

Find the 5th Term in the Binomial Expansion $( c - t ) ^ { n }$