[미적분]수렴, 발산, 극한
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Download : 10_Sequences_Infinite_Series_Improper_Integrals.hwp
sequences infinite series improper integrals
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미적분 - 수렴, 발산, 극한에 대한 영문자료(data)
[미적분]수렴, 발산, 극한
Download : 10_Sequences_Infinite_Series_Improper_Integrals.hwp( 22 )
Definition. A function f whose domain is the set of all positive integers 1,2,3.... is called an infinite sequence. The function value f(n) is called the nth term of the sequence.
Definition. A sequence {f(n)} is said to have a limit L if, for every positive number ε, there is another positive number N (which may depend on ε) such that |f(n)-L| [ ε for all n ≥ N. In this case, we say the sequence {f(n)} converges to L and we write , or f(n) → L as n→∞. A sequence which does not converge is called divergent.
Theorem 10.1. A monotonic sequence converges if and only if it is bounded.
Point. Sn = ≥ log (n+1)
Point. = 2 - .
10. Sequences, Infinite Series, Improper Integrals.
Definition. A function f whose domain is the set of all positive integers 1,2,3.... is called an infinite sequence. The function value f(n) is called the nth term of the sequence.
Definition. A sequence {f(n)} is said to have a limit L if, for every positive number ε, there is another positive number N (which may depend on ε) such that |f(n)-L| [ ε for all n ≥ N. In this case, we say the sequence {f(n)} converges to L and we write , or f(n) → L as n→∞. A sequence which does not converge is called divergent.
Theorem 10.1. A monotonic sequence converges if and only if it is bounded.
Point. Sn = ≥ log (n+1)
Point. = 2 - .
Theorem 10.2. Let ∑an and ∑bn be convergent infinite series of complex terms and let α and β be complex constants. Then the series Σ(α an + β bn) also converges, and its sum is given by the equation = α + β.
Theorem 10.3. If ∑an converges and if ∑bn diverges, then Σ(an +bn) diverges.
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