Question

Find the sum 46 +47 +48 +49+...+138 + 139.

Answer 1

Answer:

8695

Step-by-step explanation:

Took forever on calculator but I did it!

Answer 2

Answer:

8695

Step-by-step explanation:

There is a formula for adding all integers from 1 to some integer n.

$1 + 2 + 3 + ... + n = \dfrac{n(n + 1)}{2}$

In other words, to add all integers from 1 to an integer, multiply the integer by the next greater integer and divide by 2.

For example, what is

1 + 2 + 3 + 4 ?

Multiply 4 by the next integer, 5, and divide by 2.

(4 * 5)/2 = 20/2 = 10

Check: 1 + 2 + 3 + 4 = 3 + 3 + 4 = 6 + 4 = 10

We see that the formula works.

Now we need to apply that formula to this problem, but there's a little more to it.

If the problem were

1 + 2 + 3 + ... + 138 + 139, then we'd apply the formula and that would be it.

In this problem, though, we don't start the sum at 1. We start the sum at 46.

The trick here is to add all integers from 1 to 139, and then we subtract the sum of all integers from 1 to 45, so we are left with only the sum of the integers from 46 to 139.

Sum of integers from 1 to 139:

$1 + 2 + 3 + ... + 139 = \dfrac{139(139 + 1)}{2} = \dfrac{139(140)}{2} = 9730$

Sum of integers from 1 to 45:

$1 + 2 + 3 + ... + 45 = \dfrac{45(45 + 1)}{2} = \dfrac{45(46)}{2} = 1035$

Now we subtract the sum to 45 from the sum to 139.

46 + 47 + 48 + ... 138 + 139 = 9730 - 1035 = 8695

Answer: 8695