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Mathematics — Secondary School

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Successioni

Successioni

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20 lug 20261 min read

Topic — Successioni.

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39

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28 linked atoms.

39 Successioni numeriche

  • Algebra of limits for sequences
  • AP and GP compared
  • Arithmetic and geometric sequences
  • Arithmetic progression
  • Financial and graphical meaning
  • Finite limit and convergent sequences
  • Geometric progression
  • Geometric series (cross-reference)
  • GP and geometric series
  • Infinite limit, divergent and indeterminate sequences
  • Linguistic reading of the quantifiers
  • Monotone and bounded sequences
  • Relationship between sequences and real functions
  • Sequence: definition and notation
  • Sequences defined by recurrence
  • Sum of the first n terms of a GP
  • Sum of the first n terms of an AP
  • The anecdote of the young Gauss
  • The legend of the chessboard
  • The number e as a limit of a sequence
  • Theorem of bounded monotone sequences
  • Typical limits of sequences
  • Worked exercise — Binet’s formula for Fibonacci
  • n)^n
  • Worked exercise — Limits of rational sequences and roots
  • Worked exercise — Nested radical
  • 3
  • n^n

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  • Sequence: definition and notation
  • Sequences defined by recurrence
  • Arithmetic and geometric sequences
  • Arithmetic progression
  • Sum of the first n terms of an AP
  • The anecdote of the young Gauss
  • Geometric progression
  • Sum of the first n terms of a GP
  • The legend of the chessboard
  • AP and GP compared
  • GP and geometric series
  • Finite limit and convergent sequences
  • Linguistic reading of the quantifiers
  • Infinite limit, divergent and indeterminate sequences
  • Typical limits of sequences
  • Algebra of limits for sequences
  • Monotone and bounded sequences
  • Theorem of bounded monotone sequences
  • The number e as a limit of a sequence
  • Financial and graphical meaning
  • Relationship between sequences and real functions
  • Geometric series (cross-reference)
  • Worked exercise — Limits of rational sequences and roots
  • Worked exercise — The sequence n! / n^n
  • Worked exercise — Nested radical
  • Worked exercise — Sum of the geometric series with ratio 1/3
  • Worked exercise — Binet's formula for Fibonacci
  • Worked exercise — Limit of (1 - 1/n)^n