Write the Word or Phrase That Best Completes Each Statement $$1 \cdot 1 + 2 \cdot 1 + 3 \cdot 1 + \ldots + n = \frac { n ( n + 1 ) } { 2 }$$

question 166

Essay

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$1 \cdot 1 + 2 \cdot 1 + 3 \cdot 1 + \ldots + n = \frac { n ( n + 1 ) } { 2 }$$

---

Definitions:

Sample Size

The number of observations or replicates included in a statistical sample, influencing the study's precision and conclusions.

Null Hypothesis

A hypothesis that assumes no significant difference or relationship between variables, serving as the default position that indicates no effect or change.

Chi-Square Value

A statistic that measures the difference between observed frequencies and the frequencies expected under a specific hypothesis.

Observed Frequency

The actual count of instances or occurrences of a particular category or outcome in a set of data.