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W liczniku mamy sumę ciągu geometrycznego: \[ 1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2^n}=\frac{1}{1-\frac{1}{2}}=2 \] W mianowniku również mamy sumę ciągu geometrycznego: \[ 1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^n}=\frac{1}{1-\frac{1}{3}}=\frac{3}{2} \] Zatem mamy: \[ \lim_{n \to \infty} \dfrac{1+\dfrac{1}{2}+\dfrac{1}{4 ...
- Granica ciągu
Granica ciągu - definicje, przykłady, zadania z...
- Granica ciągu
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Wzory - poziom rozszerzony. Jeżeli a, b i c są liczbami dodatnimi oraz a ≠ 1 i c ≠ 1, to: n ⋅loga b = log a1 n b loga b = logc b logc a. Poniżej kilka przykładowych zastosowań tych wzorów. Więcej przykładów znajdziesz w poprzednich rozdziałach.
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Fraction Calculator. Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. + - x /.
