Select the Right Expression for the Following Sum and Prove $n$

question 38

Multiple Choice

Select the right expression for the following sum and prove that your statement is true for all natural numbers $n$ .
$$P _ { \mathrm { n } } : 3 + 6 + 9 \ldots 3 n$$

• A) \(\quad \frac { 3 n ( n + 1 ) } { 4 }\)
• B) \(\frac { n ( 3 n + 1 ) } { 2 }\)
• C) \(\quad \frac { 3 n ( n + 1 ) } { 2 }\)
• D) \(\frac { n ( 3 n + 1 ) } { 4 }\)
• E) none of the above

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