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Is there an addition counterpart to factorial?
I remember factorial as multiplying from a number to a number in increments of 1.
So, factorial 5 would be 1*2*3*4*5, for 120.
I want something like 1+2+3+4+5 so I can calculate values increasing in a set pattern of addition... I just don't know what that's called, and what the operator would be (for a calculator).
3 Answers
- O(n)Lv 58 years agoFavorite Answer
The counterpart is of course 1+2+...+n
Since n! = Product(k=1 to n)[k], it's only natural to substitute Product for Sum ;)
Both have a combinatorial meaning, too.
Product(k=1 to n)[k] = n! = the number of permutations of n items
Sum(k=1 to n)[k] = n(n+1)/2 = n choose 2 = the number of possible ways to select two out of n items (order of selection being insignificant).
- Anonymous8 years ago
It's called a triangular number. The nth triangular number is:
T_n = n(n + 1)/2 = 1 + 2 + 3 + ... + (n - 1) + n
