Difference between revisions of "User:Temperal/The Problem Solver's Resource3"
(→Rules of Summation: improve) |
(→Rules of Summation: note to self) |
||
Line 12: | Line 12: | ||
<math>\sum_{i=1}^{n} i= \frac{n(n+1)}{2}</math>, and in general <math>\sum_{i=a}^{b} i= \frac{(b-a+1)(a+b)}{2}</math> | <math>\sum_{i=1}^{n} i= \frac{n(n+1)}{2}</math>, and in general <math>\sum_{i=a}^{b} i= \frac{(b-a+1)(a+b)}{2}</math> | ||
+ | |||
+ | The above should all be self-evident and provable by the reader within seconds. | ||
<math>\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}</math> | <math>\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}</math> | ||
Line 21: | Line 23: | ||
<math> \sum_{i=1}^n i^5=\frac{n^2(n+1)^2(2n^2+2n-1)}{12}</math> | <math> \sum_{i=1}^n i^5=\frac{n^2(n+1)^2(2n^2+2n-1)}{12}</math> | ||
− | <!-- | + | <!-- eliminate useless n=4 and n=5; add proof for n=2 which easily generalizes to general n --> |
===Rules of Products=== | ===Rules of Products=== |
Revision as of 21:52, 10 January 2009
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 3. |
Summations and Products
Definitions
- Summations:
- Products:
Rules of Summation
, and in general
The above should all be self-evident and provable by the reader within seconds.
Rules of Products