Serries Flashcards
Recurrance relation
Function that describes the increasing values of a sequence
Limit of a sequence
The limit as the number of terms increases towards infinity
Lim n→∞ {a}=L
Equal to Lim n→∞ f(x)=L
Converging sequences
Has a Lim n→∞ {a}
Diverging Sequences
Has no Lim n→∞ {a}
Infinite Serries
A serries with an infinite number if terms
Nondecreasing Sequences
Each term of the sequence increases
Monotonic Sequences
Series in which the terms neither continuously increase or decrease
Bounded serries
A series whose terms are all less than or equal to a finite number
Geometric Sequence
Series in which the last term is multiplied by an unchanging number
Sequence Ratio
The unchanging number by which the terms in geometric sequence are multiplied
Squeeze Theorem for sequences
If {a}
Harmonic Sequence
Increasing denominator value by one
Σ(1/k)=1+1/2+1/3+…
Limit of zero
P-serries
Increasing denominator value by one with an exponent
Σ(1/k^p)
Limit of zero
Convergence Test
Sequence converges if the sequence limit equals zero
Ratio Test
If the ratio ‘r’ is 0<1, the sequence converges
Root test
If p= Lim k→∞ k’d√(a sub-k)
If 0<p><1, the sequence converges</p>
Comparison Test
If all the terms of series1 are greater than the terms of series2
They either converge together or diverge together