PDF version of
this article

**Next:** Bibliography **Up:** rvhtm **Previous:**
Concluding
summary

Proof that the sum of all integers less than or equal to is .

- Proof for 0: .
- Proof that if it is true for it must be true for
.
- Assume we have for any that that the sum of all integers less than is .
- Then the sum of all integers less than must be .
- Put the in the numerator of the fraction producing .
- Simplify using the common factor to get .
- Substituting for in the above equation yields .

- This completes the proof that if the equation is true for it must be true for and that completes the proof by induction.

home | consulting | videos | book | QM FAQ | contact |