If x=1^2-2^2+3^2-4^2+5^2-6^2+.........+99^2-100^2 y=1^2+2^2+3^2+4^2+5^2+.........+49^2+50^2

M4maths Previous Puzzles

11 Jun 2009 Find the equation.

If x=1^2-2^2+3^2-4^2+5^2-6^2+.........+99^2-100^2
y=1^2+2^2+3^2+4^2+5^2+.........+49^2+50^2

Then 1^2+3^2+5^2+7^2+9^2+.........+99^2 is equal to?
^ is for square

OPtion

1) x+y
2) x-y
3) x-4y
4) x+2y
5) x+3y
6) 2x-y
7) 2x-3y
8) x+4y
9) 4x-y
10) 4x+y

Solution

1^2-2^2+3^2-4^2+5^2-6^2+……………+99^2-100^2
x= (1^2+3^2+5^2+7^2+…….99^2)-(2^2+4^2+6^2+8^2+……100^2)
x= (1^2+3^2+5^2+7^2+…….99^2)-4(1^2+2^2+3^2+4^2+…………......+49^2+50^2)

Correct Option: 8 Best Solution (0)