Use Mathematical Induction to Prove That the Statement Is True $$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

question 55

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

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Definitions:

Chemical Contraception

Methods of preventing pregnancy that involve the use of drugs or chemical compounds, such as oral contraceptives.

Surgical Contraception

Methods of birth control that involve surgical procedures, typically permanent, such as tubal ligation for women or vasectomy for men.

Epididymis

A tightly coiled tube situated behind the testicles, where sperm mature and are stored.

Vas Deferens

A duct in the male reproductive system responsible for transporting sperm from the epididymis to the ejaculatory ducts.