Fandom

Math Wiki

Adding Consecutive Numbers

995pages on
this wiki
Add New Page
Talk0 Share

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

The count is easy and try but there is a faster shortcut.

You can count 1+2+3+4+5+6+... tiring right.

There a shortcut for it is to take as 1+2+3+4+...+n

First take n/2

next take n+1

then mutiply

(n/2)(n+1) is 1+2+3+...+n

n is an algebrabic unit.

try 10

10/2=5

10+1=11

5*11=55

or

take 1+2+...+n-1+n =

take half of n then add half

then take yor number after that multipy

(n/2+1/2)n

Proof:

if x = sum (1...n) then

x + (n + 1) = n * (n+1) / 2 + (n + 1)

x + (n + 1) = (n * (n + 1) + 2n +2) / 2

x + (n + 1) = ((n*n + n) + 2n + 2) / 2

x + (n + 1) = (n*n + 3 *n + 2) / 2

x + (n + 1) = ((n + 1) * (n + 2)) / 2



What if it doesn't start at 1?

Like 15+16+17+...

Minus the smaller consecutive numbers from the bigger ones.

Try from 21 to 80.

(80+1) * (80/2) - (20/2) * (20+1)

=(81 * 40) - (10 * 21)

=3240 - 210

=3030

Also on Fandom

Random Wiki