UPSC CAPF AC 2021 Paper

nth term of series ;
Tn
= 1 +

n

2

+

n2

2

T1 = 1 +

1

2

+

12

2

T2 = 1 +

2

2

+

22

2

..............
T20 = 1 +

20

2

+

202

2

Sum of series = ( 1 + 1 + 1 + ............+ 20 times )
+

1

2

(1 + 2 + ....... + 20 ) +

1

2

×

20(20+1)(40+1)

6

[1+2+3+....+n=

n(n+1)

2

‌and‌12+22+32+.....n2=

n(n+1)(2n+1)

6

]
= 20 + 105 + 1435 =1560