Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
n∈{2,3}
Evaluate
(n−1)!>(n−2)!
Find the domain
More Steps
Evaluate
{n−1∈Nn−2∈N
Calculate
n−1∈N,n−2∈N
(n−1)!>(n−2)!,n−1∈N,n−2∈N
Move the expression to the left side
(n−1)!−(n−2)!>0
Add the terms
More Steps
Evaluate
(n−1)!−(n−2)!
Calculate
(n−1)(n−2)!−(n−2)!
Calculate
(n−1−1)(n−2)!
Calculate
(n−2)(n−2)!
(n−2)(n−2)!>0
Separate the inequality into 2 possible cases
{n−2>0(n−2)!>0{n−2<0(n−2)!<0
Solve the inequality
More Steps
Evaluate
n−2>0
Move the constant to the right side
n>0+2
Removing 0 doesn't change the value,so remove it from the expression
n>2
{n>2(n−2)!>0{n−2<0(n−2)!<0
Since the left-hand side is always positive,and the right-hand side is always 0,the statement is true for any value of n
{n>2n∈R{n−2<0(n−2)!<0
Solve the inequality
More Steps
Evaluate
n−2<0
Move the constant to the right side
n<0+2
Removing 0 doesn't change the value,so remove it from the expression
n<2
{n>2n∈R{n<2(n−2)!<0
Since the left-hand side is always positive,and the right-hand side is always 0,the statement is false for any value of n
{n>2n∈R{n<2n∈/R
Find the intersection
n>2{n<2n∈/R
Find the intersection
n>2n∈/R
Find the union
n>2
Find the intersection
n>2,n−1∈N,n−2∈N
Calculate
n=2n=3
Solution
n∈{2,3}
Show Solution
