Use Mathematical Induction to Prove That the Statement Is True

question 65

Essay

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 area of the nth new
triangle. Use math induction to prove your answer.