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

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

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

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

Question

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

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

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

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

Quizplus · Accepted Answer

The rth term in the binomial expansion of (c+y)^n is given by the term containing c^(n-r+1) and y^(r-1). We see that option D is the only one that satisfies this condition, so it is the best choice. The formula in option D is derived from the general formula for the rth term in the binomial expansion, which is (n choose r) * a^(n-r) * b^r, where a and b are the terms being raised to powers in the binomial and (n choose r) is the binomial coefficient. Plugging in a=c and b=y, we get the formula in option D.

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

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