When many of us think of the word "arithmetic", our mind conjures up an image of a sheet of endless multiplication facts told by our teachers to learn, practice, memorize, again. But arithmetic can get more interesting. What if I gave you the problem:
Find the sum of all the numbers from 1 to 100, inclusive. Or in other words,
Calculate the sum of 1 + 2 + 3 . . . . . + 98 + 99 + 100.
How would you approach it? I certainly hope you wouldn't bide your time and just add 100 numbers mindlessly! Especially after I tell you this slick trick:
The formula for finding the sum of an arithmetic sequence (a sequence that has a constant common difference; in this case; 1) is:
Find the sum of all the numbers from 1 to 100, inclusive. Or in other words,
Calculate the sum of 1 + 2 + 3 . . . . . + 98 + 99 + 100.
How would you approach it? I certainly hope you wouldn't bide your time and just add 100 numbers mindlessly! Especially after I tell you this slick trick:
The formula for finding the sum of an arithmetic sequence (a sequence that has a constant common difference; in this case; 1) is:
Let's apply it.