Suppose You Wish to Prove That the Following Is True

question 31

Essay

Suppose you wish to prove that the following is true for all positive integers n by using mathematical induction:
1+3+5+...+(2 n-1)=n²
(a) Write P(1).
(b) Write P(72).
(c) Write P(73).
(d) Use P(72) to prove P(73).
(e) Write P(k).
(f) Write P(k + 1).
(g) Use mathematical induction to prove that P(n) is true for all positive integers n.

---

Definitions:

Total Lung Capacity (TLC)

The maximum amount of air the lungs can contain, typically measured after a maximal inhalation effort.

Spirometer

An instrument used to measure the volume of air inhaled and exhaled by the lungs, assessing pulmonary function.

Functional Residual Capacity (FRC)

The amount of air left in the lungs following a standard breath out.

Residual Volume (RV)

The volume of air remaining in the lungs after a maximal exhalation, important for keeping the lungs inflated.