Use the Principle of Mathematical Induction to Prove That $$1 + 4 + 7 + 10 + \cdots + ( 3 n - 2 ) = \frac { n ( 3 n - 1 ) } { 2 } \text { for all }$$

question 6

Short Answer

Use the Principle of Mathematical Induction to prove that $$1 + 4 + 7 + 10 + \cdots + ( 3 n - 2 ) = \frac { n ( 3 n - 1 ) } { 2 } \text { for all }$$ n ≥ 1.

---

Definitions:

Automatic Processing

The subconscious processing of information, allowing tasks to be performed without conscious effort or attention.

Ebbinghaus

A psychologist who pioneered the experimental study of memory and is best known for his discovery of the forgetting curve and the spacing effect.

Forgetting Curve

A graphical representation of the decline in memory retention over time, showing how information is lost when there is no attempt to retain it.

Newly Learned Information

Knowledge or data that has been recently acquired through learning or education.