For Each Integer $n \geq 3$ , Let $P ( n )$

question 8

Essay

For each integer $n \geq 3$ , let $P ( n )$ be the equation
$3+4+5+\cdots+n=\frac{(n-2)(n+3)}{2} \cdot \leftarrow P(n)$
(Recall that by definition $3 + 4 + 5 + \cdots + n = \sum _ { i = 3 } ^ { n } i _ {. }$ )
(a) Is $P ( 3 )$ true? Justify your answer.
(b) In the inductive step of a proof that $P ( n )$ is true for all integers $n \geq 3$ , we suppose $P ( k )$ is true (this is the inductive hypothesis), and then we show that $P ( k + 1 )$ is true. Fill in the blanks below to write what we suppose and what we must show for this particular equation.
Proof that for all integers $k \geq 3$ , if $P ( k )$ is true then $P ( k + 1 )$ is true:
Let $k$ be any integer that is greater than or equal to 3 , and suppose that___ We must show that________
(c) Finish the proof started in (b) above.

Grasp the requirements for disclosing earnings per share and other key financial items in interim reports.

Become familiar with the disclosure requirements under International Financial Reporting Standards (IFRS) for interim reporting.

Analyze the effects of inventory valuation method changes on interim financial reporting.

Understand and apply principles of taxation allocation within financial periods.

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Definitions:

Autonomy

The capacity to make an informed, uncoerced decision; in psychology, it often relates to the sense of control or agency over one's actions and life.

Relatedness

The feeling of being connected or related to others, which is essential for fostering social bonds and personal relationships.

Existence Needs

Basic physical and material well-being necessities like food, shelter, and safety that individuals require.

Growth Needs

Psychological requirements that drive personal development, self-improvement, and the fulfillment of one's potential.