=861 ⇒n2+n−1722=0 ⇒n2+42n−41n−1722=0 ⇒n(n+42)−41(n+42)=0 ⇒(n+42)(n−41)=0 ⇒n=−42,41 Thus, there are exactly two values of n for which Sn=861. Hence, statement 1 is correct. Sn=S−(n+1)
⇒
n(n+1)
2
=
−(n+1)(−n−1+1)
2
⇒n=n This is true for all values of n. For m=–1,
n(n+1)
2
=−1⇒n2+n+2=0 But, there exists no real integral value of n which satisfies this equation. Hence, statement 2 is incorrect.