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:
4
Step-by-step explanation:
Because i divided 4 2/3 by 22 1/6 = 4.75 and for full sheets it would be 4
Hope This Helped
Answer:
I am pretty sure it is the second option
Step-by-step explanation:
Hope this helps
What is supposed to be the underlined digit
Answer:
q¹²
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Exponential Rule [Powering]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
(q⁶)²
<u>Step 2: Simplify</u>
- Exponential Rule [Powering]: q⁶⁽²⁾
- [Exponents] Multiply: q¹²
