Statement 1 :
The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+….+(361 +380 +400) is 8000
Statement 1:
`Sigma_(k=1)^(n) (k^3-(k-1)^3)=n^3`, for any natural number n.

Options

A. Statement 1 is fasle ,statement 2 is true
B. Statement 1 is true ,statement 2 is true , statement 2 is a correct explanation for statement 1.
C. Statement 1 is true, statements 2 is true statement 2 is not a correct explanation for statement 1
D. Statement 1 is true, statement 2 is false

Answer

B

Explanation

`T_(n)=(n-1)^(2)+(n-1)n+n^(2)`
`=((n-1)^(3)-n^(3)))/((n-1)-n)=n^(3)-(n-1)^(3)`
`T_(1)=1^(3)-0^(3)`
`T^(2)=2^(3)-1^(3)`
. . .
. . .
. . .
. . .
`T_(20)=20^(3)-19^(3)`
Adding, `S_(20)=20^(3)-0^(3)=8000`