Use Mathematical Induction to Solve for All Positive Integers N $1 + 2 + 3 + 4 + \ldots + n = ?$

question 217

Multiple Choice

Use mathematical induction to solve for all positive integers n. $1 + 2 + 3 + 4 + \ldots + n = ?$

• A) \(\frac { n ( n + 1 ) } { 2 }\)
• B) \(\frac { ( n + 1 ) } { 2 }\)
• C) \(\frac { n } { 2 } ( 3 n + 1 )\)
• D) \(\frac { n ( n + 1 ) ( 1 n + 1 ) } { 6 }\)
• E) \(\frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 3 }\)

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Definitions:

Shading

The technique in drawing and art of adding darkness to convey the sense of depth, volume, or to create the illusion of shadow.

Noncontradictory Propositions

Statements or claims that do not contradict each other, meaning they can both be true at the same time in the same context.

Nonequivalent

Not equal in value, measure, force, effect, significance, etc.; lacking equivalence or equality.

Obverse

The proposition that results from changing the quality of a categorical proposition and replacing the predicate term with its complement.