Series (inglés)
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Definición Nivel 1
The sum of a given number of terms in a sequence
Consider the sequence 1, 3, 5, 7, 9, 11, 13, 15..... the sum of the first five odd numbers is 1+3+5+7+9 = 25
Consider the sequence 1, 8, 27, 64, 125, 216..... The sum of the first four cube numbers is 1+8+27+64 = 100
Consider the sequence 1, 3, 5, 7, 9, 11, 13, 15..... the sum of the first five odd numbers is 1+3+5+7+9 = 25
Consider the sequence 1, 8, 27, 64, 125, 216..... The sum of the first four cube numbers is 1+8+27+64 = 100
Definición Nivel 3
A sequence where the nth term is the sum of the first n terms of another sequence. Eg the sequence of whole numbers:
1, 2, 3, 4, 5, 6, 7 ... gives the series
1, 3, 6, 10, 15, 21, 28 ... (the triangular numbers).
1, 2, 3, 4, 5, 6, 7 ... gives the series
1, 3, 6, 10, 15, 21, 28 ... (the triangular numbers).
Relaciones
- Más general:
- (en) Sequence
- Más específico:
- (en) Alternating series
- (en) Arithmetic series
- (en) Asymptotic series
- (en) Geometric series
- (en) Infinite series
- (en) Sum of cubes
- (en) Sum of integers
- (en) Sum of reciprocals of fourth powers
- (en) Sum of reciprocals of odd squares
- (en) Sum of reciprocals of squares
- (en) Sum of squares
- Referencia:
- (en) Analysis
- (en) Calculus
- (en) Number patterns
- Referenciado en:
- (en) Absolute convergence
- (en) Fourier's theorem
- (en) Infinite product
- (en) Ratio test
- (en) Test for convergence
Financiado por: Socrates Minerva UE, HeyMath!, Cambridge University Press