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?

Step-by-step solution

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