Question

For whole numbers between 1 and 1001, inclusive, let m be the sum of odd numbers and n be the sum of even numbers. What is the value of m−n?

Answer 1

Answer:

m - n = 501

Step-by-step explanation:

Remark

The first thing you have to do is find the number of odd and even numbers. This is where you have to be careful because there is a danger of being out by one.

equation

l = a + (n - 1)*d

Solution even

l = 1000

a = 2

d = 2

1000 = 2 + (n - 1)*2

998/2 = (n - 1) * 2 / 2

499 =  n - 1

n = 500

Solution odd

l = 1001

a = 1

d = 2

1001 = 1 + (n - 1)*2

1000 =  (n - 1)*2

1000/2 =  (n - 1)2/2

500 =  n - 1

501 = n

Sum Even of even numbers from 1 to 1001

Givens

a = 2

n = 500

l = 1000

Equation

Sum = (a + l ) * n / 2

Solution

Sum = (2 + 1000)*500/2

Sum = 1002 * 250

Sum = 250500

Sum of Odd numbers from 1 to 1001

a = 1

l = 1001

n = 501

Equation

sum = (a + l)*n/2

sum = (1 + 1001) * 501

sum = (1002)*501 / 2

Sum =  251001

Answer

m - n = 251001 - 250500 = 501