A Statement Sn About the Positive Integers Is Given $$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

question 159

Essay

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
- $$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

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Definitions:

Payback Method

A capital budgeting technique that calculates the time required to recoup the cost of an investment, focusing on cash flow rather than profitability.

Time Value

The idea that having money now is more valuable than having the same amount later because of the possible income it can generate.

Obsolescence

The process of an asset becoming outdated or no longer used, often due to technological advancements.

Annual Rate of Return

The Annual Rate of Return is the percentage of profit or loss on an investment over a one-year period, taking into consideration both capital gains and dividends.