Use Mathematical Induction to Prove That the Statement Is True

question 319

Short Answer

Use mathematical induction to prove that the statement is true for every positive integer n.
-The series of sketches below starts with an equilateral triangle having sides of length 1
(one). In the following steps, equilateral triangles are constructed by joining the midpoints
of the sides of the preceding triangle. Develop a formula for the length of the sides of the
new triangle.

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Definitions:

Guard Cells

Specialized cells in the epidermis of leaves, stems, and other organs that regulate gas exchange and water loss by controlling the opening and closing of stomata.

Stomata

Tiny openings or pores found in the epidermis of leaves and stems that allow for gas exchange between the plant and its environment.

Palisade Mesophyll

The layer of closely packed cells in a plant leaf where most photosynthesis occurs.

Upper Epidermis

The outermost layer of cells in the upper part of a plant leaf or stem, serving as a protective barrier against the environment.