1 + 3 + 5 + 7 + 9 = 25
25 ÷ 5 = 5
The answer is 5
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:
8x + 1/2 or 8x + 0.5
Step-by-step explanation:
-6x + 3 3/4 + 14x - 3.25
u can either convert the fraction to a decimal or convert the decimal into a fraction, i'm going to do the latter
-6x + 3 3/4 + 14x - 3 1/4
rearrange to make it easier, don't need to do this i'm just doing this for the sake of it
-6x + 14x + 3 3/4 - 3 1/4
8x + 2/4, simplify this
8x + 1/2
The decimal way if u want:
-6x + 3 3/4 + 14x - 3.25
-6x + 3.75 + 14x - 3.25
-6x + 14x + 3.75 - 3.25
8x + 0.5
