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
Answer:
A gotchu Just took the test got 100
Step-by-step explanation:
B
<span>The equation of the line that passes through the point (0,5) with a slope of 1/2</span>
<span>y=1/2x+5</span>
The next score is 90 because 85+91+92+92=360/4= 90 average.
You would put 8 where x is and -10 where y is and then you will do -10 to the second power, which you will get 100 and so you will get 104. The answer is
D) 104
