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:
The answer is 337.5.
Step-by-step explanation:
Srry Im late. :(
5/6 is equivalent to 20/24
3/4 is equivalent to 18/24
so 5/6 is bigger than 3/4 by 2/24
9514 1404 393
Answer:
0
Step-by-step explanation:
The function is defined everywhere except at x=-6. The limit value is the function value at that point.
f(6) = (6^2 -36)/(6 +6) = 0/12 = 0
The limit of the function is 0 as x → 6.
