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Sequence, Series is a sum of terms of sequence - Coggle Diagram
Sequence
Series
Infinite
S∞ = U1 / (1-r ), ∣r∣<1
A sequence with terms that tend to
Zero are called convergent
Sigma
∑
Number upon ∑: Ending term
Number under ∑: starting term
Formula beside ∑: Rule to generate the terms we are adding
Arithmetic
Geometric
Sn = U1(1-r^n) / 1-4 = U1(r^n-1) / r-1
Arithmetic
common difference = d
Explicit Rule
General Term
Un = U1 + (n-1)d
Recursive Definition
Un+1 = Un + d
Un = Un-1 +d
Geometirc
Explicit Rule
General Term
Un=U1r^(n-1)
common difference = constant ratio : r = U2/U1 = U3/U2 ... = Un+1/Un
Recursive Definition
Un = rUn-1 OR Un+1 = rUn
Definiton
Recursive
how to generate the next term (Un+1, Un-1)
Explicit
Sequence
An ordered list of numbers
Pattern
Linear
first common difference between consecutive terms
Un = An + b
Recursive Definition
Un+1 = Un+a
Quadratic
Involve square numbers
a=second difference/2
Series is a sum of terms of sequence