? asked in Education & ReferenceHomework Help · 10 years ago

# How do you find the sum of all numbers from 1 to 100 by using patterns and combinations & shorter easier way?

It's for my son's hw this is what the page states

"The objective of this activity is to find the sum of all the counting numbers from 1 to 100. You could certainly add 1 + 2 + 3 continuing to 100 to find the sum. However, this is too much work for this problem. If you can look for patterns and combinations, you can find a much shorter and easier way to solve this problem. Try to work smarter, not longer.

Answer 1 plus all the numbers up to 100 __________

now sum 1 to 200 as well

Answer 2 plus all the numbers up to 200 __________

Relevance
• 10 years ago

Hey!

To find the sum of consecutive integers, you must first find the middle number. To do this, you add the first and last number, and divide by two.

1 + 100 / 2 = 55.5

Next, you must find the number of numbers (last number - first number + 1), which is 100 in this case.

And finally, you simply multiply the two numbers together.

55.5*100 = 5550

Therefore the sum of all the numbers is 5550!

Source(s): Hope that helps!
• Anonymous
10 years ago

This is the formula:

(1 + n)*(n/2)

n = The number of numbers

So:

Up to 100: (1+100)* (100/2) = 101*50 = 5,050

Up to 200: (1+200)*(200/2) = 201*100 = 20,100

Source(s): A* Maths iGCSE