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 115

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:

Zero Coupon

A type of bond that does not pay periodic interest payments but instead is sold at a deep discount from its face value and pays its full face value at maturity.

Imputed Interest

The assumed interest rate used by the IRS for tax purposes on loans with little or no interest, to ensure that tax is collected on essentially interest-free loans.

Call Provision

A clause in a bond's contract that allows the issuer to redeem the bond before its maturity date under specific conditions.

Retire Bonds

The process of paying off or redeeming bonds before or at maturity to eliminate debt obligations.