Glad I chose this one

I thought sure I posted something like this before, but apparently not. (I cycled through the “grids” of all my November and December posts.)

But, you see, this is what happens when you ask an applied mathematician to unwrap a designated number of chocolate kisses, 33 in this case… (BTW, After “assembly”)

Of course, everyone knows the shortcut for adding up 1 + 2 + 3 + … + n, right?
The formula is often easy to do in your head: ½ × n × (n+1).

There is a famous story about one of history’s greatest mathematicians involving this formula. The teacher assigned his class the task of adding up the first 100 integers, figuring this would keep everyone busy for a period of time.

But while everyone else was doing the tedious addition by longhand, 7-year old Karl Friedrich Gauss looked at the problem in a completely novel way. He saw an obvious pattern and solved the problem quite quickly.

He worked from the outside inward, pairing numbers together:

      1    +   2 +   3 + … + 50
     100 + 99 + 98 + … + 51

Written in this way, it’s clear that the complete sum from 1 to 100 is fifty pairs of 101! The result can be reduced to a general formula so that the desired result is:

     1 + 2 + … + 100 = ½ × 100 × 101 = 50 × 101 = 5000 + 50 = 5050.

» An excellent visual explanation of how Gauss saw it
» A more scientific explanation

Looking back
  1 year ago: “Doll bed, ‘After’”
 2 years ago: No post
 3 years ago: No post
 4 years ago: “Last one [filler]”
 5 years ago: No post
 6 years ago: “Every project deserves a new tool.”
 7 years ago: “More than 4 weeks behind posting. Any other questions?” (Four weeks? Hahahaha!)
 8 years ago: “Looking for Dilbert…”
 9 years ago: “Speaking of ‘bracts’”
10 years ago: “Angels”

[ PXL_20211204_160643643SOOC675x9tm :: cell phone ]

[Mags]

LOL! Good one!

[Esther Rosenberg]

Perfect pattern! You totally lost me with all those numbers. My middle son is a math genie..he loves this stuff. Obviously, not getting that from me :)

[Jane Pittenger]

Lol

[Thom Mitchell]

@dutchothotmailcom This is a formula your son should know. :) Also, the formula is often used to illustrate the proof method known as “mathematical induction”: see https://en.wikipedia.org/wiki/Mathematical_induction#Sum_of_consecutive_natural_numbers