If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true? Pick.
A) S is always odd. B) S is always even. C) S must be a prime number D) S must not be a prime number E) S must be a perfect square
If n &gt; 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?   A. S is always odd.   B. S is always even.   C. S must be a prime number   D. S must not be a prime number   E. S must be a perfect square   Notice that we are askedwhich of the following MUST be true, not COULD be true. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   A. S is always odd --&gt; not necessarily true if n=3 then 1+2+3= 
<gadget id="calculator">1+2+3</gadget>
<output>6</output>
6=even.   B. S is always even --&gt; not necessarily true if n=5 then 1+2+3+4+5= 
<gadget id="calculator">1+2+3+4+5</gadget>
<output>15</output>
15=odd.   C. S must be a prime number --&gt; not true if n=3 then 1+2+3= 
<gadget id="calculator">1+2+3</gadget>
<output>6</output>
6=not prime.   E. S must be a perfect square --&gt; not necessarily true if n=3 then 1+2+3= 
<gadget id="calculator">1+2+3</gadget>
<output>6</output>
6=not a perfect square.   Only choice D is left.   Answer: S must not be a prime number.
<result>D</result>
If n > 2, then the sum, S, of the integers from 1 through n can be calculated by the following formula: S = n(n + 1)/2. Which one of the following statements about S must be true?