Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Number of cups you have / number of friends to share it between = 6/8
You can simplify 6/8 by dividing both the numerator and the denominator by 2.
6/8 = 3/4 or 0.75 of a cup
DSM stands for Diagnostic and Statistical Manual of Mental Disorders. DSM is aclassification system for the mental disorders and indicates how the disorder can be distinguished from other. The DSM-5 recognized anxiety disorders are: generalized anxiety disorder, phobic disorder, panic disorder and obsessive compulsive disorder. <span>Approximately 3 percent of the population are diagnosed with panic disorder using DSM criteria.</span>
Numerical because its the number of assistants.
The area of the mat is 42.67 inches^2 or 42 and 2/3 in^2
