UPSC NDA Math Model Paper 10

Let the nth term and sum of the series upto n terms of the series be Tn and Sn , respectively. Then,
⇒Sn=

1

5

+

3

5

+1+

7

5

+

9

5

+.......
Multiplying the above equation by 5, we get
⇒5Sn=1+3+5+7+9+....... up to n terms
This is the sum of first odd natural numbers.
As we know that, sum of the first n odd natural numbers i.e 1 + 3 + 5 +7 +9 + ...up to n terms = n
⇒ ⇒5Sn=n2⇒Sn=n2∕5
For n=50,S50=502∕5=500.
Hence, option 2 is the correct answer.