for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?
since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e
multiply(add(add(add(add(add(add(add(multiply(const_4, 2), subtract(multiply(const_4, 2), const_1)), subtract(multiply(const_4, 2), const_2)), subtract(multiply(const_4, 2), const_3)), subtract(multiply(const_4, 2), const_4)), subtract(multiply(const_4, 2), subtract(multiply(const_4, 2), const_3))), subtract(multiply(const_4, 2), subtract(multiply(const_4, 2), const_2))), subtract(multiply(const_4, 2), subtract(multiply(const_4, 2), const_1))), add(add(add(multiply(2, const_2), subtract(multiply(2, const_2), const_1)), subtract(multiply(2, const_2), const_2)), subtract(multiply(2, const_2), const_3)))