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:
5
Step-by-step explanation:
4 7/12 + 5/12 = 4 12/12 which equals 5
The correct question in the attached figure
we know that
to fill the tank is required--------> 100%-20%--------> 80%
if 20% of the gas tank is-----------------> 288.75 gal
80% --------------------------------------> X gal
X=80*288.75/20--------> X=1155 gal
if 1 gal----------------> cost $3
1155 gal----------> $X
X=1155*3--------> X=$3465
the answer is
the cost to fill the tank is $3465
Answer:
46
Step-by-step explanation:
180 minus 105 minus 29