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:
firstly you know the term of multiplication
like 5*2=10 ,10*2=20, 20*2 =40 and 40*2 =80
and last three numbers are 80, 160,320
Answer:
-24
Step-by-step explanation:
I´m guessing by the big x sign you want me to multiply so the first step in the equation is to multiply because of PEMDAS so(6*2)+(8*-3)-3*2-6,
so 6*2=12,8*-3=-24,-3*2=-6
12+-24-6-6,
12-24=-12,-6+-6=-12
-12+-12=-24
Step-by-step explanation:
this is the answer key for that question and etc...
There are 10 letters in the set {a, b, c, d, e, f, g, h, i, j} which is the pool of letters to choose from when making these three letter codes.
We have 10 choices for slot 1
Then 9 choices for slot 2. This is because we can't reuse the choice for slot 1
Then 8 choices for slot 3
Overall, there are 10*9*8 = 90*8 = 720 different permutations
Answer: 720
Note: you can use the nPr permutation formula with n = 10 and r = 3 to get the same answer
