Number System

Fast trick to solve number system

Q .Solve (12 - 22 + 32 - 42 + 52 - 62 + 72 - 82 + 92 - 102) = ?

As we see we can use formula of -

a2 - b2 = ( a + b ) ( a - b )

= ( 1 + 2 )( 1 - 2 ) + (3 + 4 )( 3 - 4 ) + (5 + 6)( 5 - 6) + ( 7 + 8)( 7 - 8 ) + (9 + 10)(9 - 10)

= ( -3 ) + (-7 ) + (-11) + ( -15 ) + (-19)

= -3 -7 -11 -15 -19

= -55

? = -55