The sum of the n terms of the series 121.3+223.5+325.7+.....+n2(2n-1)(2n+1) is
n(n+1)2(2n+1)
(2n2+1)(2n+1)
(2n2+1)4(2n+1)
None of these
Find the sum of the given series
121.3+223.5+325.7+.....+n2(2n-1)(2n+1)
Here, tn=n2(2n-1)(2n+1)
⇒tn=14+18(2n-1)-18(2n+1)
Let the sum of the given series be Sn
⇒Sn=n4+181-13+13-15+15+........-12n-1+12n-1-12n+1⇒Sn=n4+181-12n+1⇒Sn=n4+n4(2n+1)⇒Sn=n42n+22n+1⇒Sn=nn+12(2n+1)
Hence, the correct option is OptionA.
limn→∞[11.3+13.5+15.7⋯1(2n+1)(2n+3)] is equa to