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
Find out smarty don’t cheat
Answer:
2√5
Step-by-step explanation:
d = √(x2 - x1)² + (y2 - y1)²
= √[1 - (-1)]² + [3 - (-1)]
= √(2)² + (4)²
= √(4) + (16)
= √20
= 2√5
Answer:
A number cubed plus a 3 times a number squared all multiplied by 2 is equal to 4 times a number.
Step-by-step explanation:
Since we can't say "in parenthesis", we will have to say the expressions in the parenthesis first and then say "all multiplied by 2" to express parenthesis in word form. The rest are pretty straight forward.
