UPSC NDA Math Model Paper 5

Statement – 1
Sum of cubes of first n consecutive natural numbers is given by (

n(n+1)

2

)2
We have n=15
∴Sum=(

15(15+1)

2

)2
=(

15×16

2

)2
=(120)2
=14400
So, this statement is correct.
Statement −2
Sum of squares of first n consecutive natural numbers is given by (

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

6

)
We have, n=20
Sum=(

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

6

)
=(

20(21)(41)

6

)
=10×7×41
=2870
This statement is not correct.
Hence, option (1) is correct.