You can try to show this by induction:
• According to the given closed form, we have 
, which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume
and
We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or
From the given recurrence, we know
so that
which is what we needed. QED
Answer:
x = 1/3
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
4x + 1 = 3 - 2x
<u>Step 2: Solve for </u><em><u>x</u></em>
- Add 2x on both sides: 6x + 1 = 3
- Subtract 1 on both sides: 6x = 2
- Divide 6 on both sides: x = 1/3
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: 4(1/3) + 1 = 3 - 2(1/3)
- Multiply: 4/3 + 1 = 3 - 2/3
- Add/Subtract: 7/3 = 7/3
Here we see that 7/3 does indeed equal 7/3.
∴ x = 1/3 is a solution of the equation.
Answer:
-8 I believe
Step-by-step explanation:
Answer :
Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.
Since, a, b and 3 are integers. So,
Here, it contradicts that √5 is an irrational number.
because of the wrong assumption that 3 + √5 is a rational number.
Hence, 3 + √5 is an irrational number.
