Use Mathematical Induction to Prove That $1 + 2 ^ { n } \leq 3 ^ { n } \text { for all } n \geq 1$

question 48

Essay

Use mathematical induction to prove that $1 + 2 ^ { n } \leq 3 ^ { n } \text { for all } n \geq 1$

---

Definitions:

Fraternal Twins

Twins that develop from two different eggs fertilized by two different sperms, resulting in genetically unique siblings born at the same time.

Gender Constancy

Gender constancy is the understanding in children that one's gender remains the same over time and across situations, typically developed by the age of six or seven.

Cognitive Development

The progression of learning and processing of information from infancy through adulthood, encompassing skills in perceiving, thinking, and understanding.

Gender Stereotypes

Gender stereotypes are generalized beliefs or preconceptions about characteristics, attributes, and behaviors traditionally associated with men and women.