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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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A geometric progression is a sequence in which each term (after the first) is determined by multiplying the preceding term by a constant. This constant is called the common ratio of the geometric progression. The following equations express this statement mathematically, an+1
= an·q,
an = a1· q n-1, where a1 is the first term of the progression; an is its nth term; q is the common ratio of the geometric progression; n is a natural number. Let us calculate the sum of the first n terms of the geometric progression:
Note that
Therefore,
If | q | <
1 then qn
→ 0 as n → ∞.
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