(New page: <math>J(\vec{w}) = \frac{\vec{w}^t S_B \vec{w}}{\vec{w}^t S_W \vec{w}} </math>) |
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| − | <math> | + | * (a) Prove that <math>1 + x + x^2 + \ldots + x^{n-1} = \frac{1-x^n}{1-x}</math> for <math>x\neq1</math> and integer <math>n\geq1</math>. |
| − | </math> | + | |
| + | * (b) What is <math>1 + 2x + 3x^2 + \ldots +nx^{n-1}</math>? (Hint: differentiate (a)) | ||
Revision as of 17:24, 3 September 2008
- (a) Prove that $ 1 + x + x^2 + \ldots + x^{n-1} = \frac{1-x^n}{1-x} $ for $ x\neq1 $ and integer $ n\geq1 $.
- (b) What is $ 1 + 2x + 3x^2 + \ldots +nx^{n-1} $? (Hint: differentiate (a))
