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| Discrete Algebra |
 Sigma-Notations Arithmetic Progressions Geometric Progressions Binomial Theorem Pascal's Triangle
1 + 2 + ... + n 1² + 2² + ... + n² 1³ + 2³ + ... + n³
Basic Conceptions Constituents of the Induction Principle Model Examples Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 |
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The Binomial Theorem gives a simple way of expanding expressions of the form (a + b)n:
We need only to calculate the binomial coefficients Cnk
with k = 0, 1, … n. Cn0
= 1 and Cnn = 1,
Cn1 = n and Cnn–1 = n, etc. Moreover, the binomial coefficients satisfy the following recursion relationships:
It means that a binomial coefficient with subscript n
+ 1 and superscript 0 < k
< n is the sum of the corresponding
coefficients whose subscripts have preceding value n .
Comment 1. All boundary
coefficients are equal to unity.
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