Consider the following statements : 1. 2+4+6+ +2 n=n^2+n 2. The expression n^2+n+41 always gives a prime number for every natural number n Which of the above statements is/are correct?

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Correct answer: A. 1 only

Let S=2+4+6+ +2 n=2(1+2+3+ +n)=2 · (n(n+1))/(2)=n^2+n Statement 1 is true. Putting n=41 in n^2+n+41=41^2+41+41=41.(41+2)=41.43 Which is not prime. So, expression not always prime for n ∈ N

Consider the following statements : 1. 2+4+6+ +2 n=n^2+n 2. The...

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