| Tired of seeing ads? Click here to upgrade to Elite Membership! |
Mathematics Forum
|
| Author | Message / Information |
| abiy3000 Quote | Reply | | summation of powers of consecutive integers posted on: 9/2/2006 5:37:22 AM hi, is there a general formula for (1^n+2^n+3^n+...+r^n)? |
|
illoyd
Quote | Reply | |
summation of powers of consecutive integers
replied on: 9/4/2006 3:22:31 PM Sums of Powers Let Sk[N] denote the sum of the kth powers of the first N integers. Most people are familiar with the formulas for the first few sums S1[N] = N(N+1)/2 S2[N] = N(N+1)(2N+1)/6 S3[N] = N^2 (N+1)^2 /4 S4[N] = N(N+1)(2N+1)(3N^2+3N-1)/30 etc. The general formula can be expressed as B_(k+1)[N+1] - B_(k+1)[0] Sk[N] = -------------------------- k+1 |
|
illoyd
Quote | Reply | |
summation of powers of consecutive integers
replied on: 9/4/2006 3:27:52 PM Try again The general formula can be expressed as Sk[N] = (B_(k+1)[N+1] - B_(k+1)[0])/k+1 where B_n[x] denotes the nth Bernoulli polynomial. There are several interesting methods for deriving these formulas. Around 1690 Jacques Bernoulli gave a nice description of his derivation in a short paper where he introduced the "Bernoulli Numbers". |
|
LinkBot
|
Gamers Wanted is looking for people to write game reviews and post news, |
|
|
| Tired of seeing ads? Click here to upgrade to Elite Membership! |
ChatArea.com Help & News Forums | Terms of Use | Contact ChatArea.com | Advertising
Powered By ChatArea.com - Get your free Society today! © Copyright 2003 Wewp!