(1995-1993)x(1993-1991)x(1991-1989)x...x(5-3)x(3-1)=

Question

A) 2X996

B) 2X997

C)2⁹⁹⁶

D) 2⁹⁹⁷

Please explain step by step.

Answer 1

If you notice, each of those parenthesis equals 2... when you multiply 2 by 2, it becomes 2². Thus, if you know there are 'n' groups of parenthesis, then the answer is '2ⁿ'

You can see that the numbers are sequential. Looking at the 2nd term in each set, we see that it goes from 1 to 1993, doing only odd numbers. Thus, if we subtract the 2 numbers and divide by 2, we will the number of odd numbers between the numbers, including the last number. We then add 1 to account for the beginning number.

# of terms = (last - first) / 2 + 1

# of terms = (1993 - 1) / 2 + 1

# of terms = (1993 - 1) / 2 + 1

# of terms = 997

Answer = 2⁹⁹⁷

Answer 2

1995 - 1 = 1994

There are 1994/2 = 997 pairs of odd numbers decreasing by 2 within each pair.

The product of all these differences of 2 is D), 2⁹⁹⁷