If n is odd, then 1+3+5+7+.....+ to n terms is equal to
(a) (n2+1)
(b) (n2−1)
(c) n2
(d) (2n2+1)
Consider, 1+3+5+7+.....+ to n terms
Here, a=1,d=5−3=3−1=2, therefore, the given series is an AP.
Therefore, using sum of n terms of an AP, we get,
⇒Sn=n2[2a+(n−1)d]
⇒Sn=n2[2(1)+(n−1)(2)]
⇒Sn=n[1+(n−1)]
⇒Sn=n2
Therefore, sum of n terms of an odd series is n2.