Question

(n+1)^3-n^3=1+3 (n+1)n using this formulae find the cube of 999.If cube of 1000 is 1000000000.

Answer 1

We use the formula: ( a - b )^3 = a^3 - b^3 - 3ab( a - b);

a = 1000; b = 1;

999^3 = 1000^3 - 1^3 - 3·1000·1( 1000 - 1 ) = 1000000000 - 1 - 3000·999 = 1000000000 - 1 - 2997000 = 997002999;