Put the following statements into order to prove the summation formula P(n) = (Ci1i= n(n+1) for all n ≥ 1. Put N next to the statements that should not be used:
1. The statement is true for n = 1 because in that case, both sides of the equation are 1.
2. Now suppose we have proved the statement P(n) for some n ≥ 1. Xi1i+(+1)-Xitii= n(n+4 + (n +1)
3. Now suppose we have proved the statement P(n) for all n > 1.
4. By adding n + 1 to both sides of P(n), we get Xi1i+(+1)=Xitli= 96+42 + (+1)
5. By adding +1 to both sides of P(n), we get
6. We simplify the right side: "(7+l + (n +1) = (n + 1)(2 +1) = (n+Jn+2)
7. Thus we have proved the statement P(n+1) = (L;+! i = (46+2)
8. The statement is true for n = 1 because in that case, both sides of the equation are 0.