define
- define
- And the item before NNN
- Determine convergence
- Sum: sum of the first n terms as n→∞n\to \inftyn→∞
- diverse series has no sum
Classic series
- Geometric series geometric
- Harmonic series harmonic
- collapsing series
The nature of the
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∑ n = 1 up \ sum ^ \ infty_ {n = 1} ∑, n = 1 up convergence is lim n – > + up an = 0 \ lim_ {n \ \ infty} to + a_n = 0 limn – + up an = 0
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Lim n – > + up an = 0 \ lim_ {n \ \ infty} to + a_n = 0 limn – + up an = can’t launch ∑ 0 n = 1 up \ sum ^ \ infty_ {n = 1} ∑ n = 1 up convergence
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Series are linear (additivity and multiplicability)
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The sum of convergent series converges, but the sum of divergent series does not necessarily diverge