nth term of the given series =Tn=(n−1)2+(n−1)n+n2 =
((n−1)3−n3)
(n−1)−n
=n3−(n−1)3 ⇒Sn=
n
∑
k=1
[k3−(k−1)3] ⇒8000=n3 ⇒n=20 which is a natural number. Now, put n=1,2,3,.....20 T1=13−03 T2=23−13 T20=203−193 Now, T1+T2+....+T20=S20 ⇒S20=203−03=8000 Hence, both the given statements are true and statement 2 supports statement 1 .