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38 Cards in this Set

  • Front
  • Back
converges
the infinite geometric series has a sum
diverges
the infinite geometric series has no sum
series
indicated sum of the terms of a sequence
arithmetic series
the sum of the terms in an arithmetic sequence
geometric series
the sum of the terms in a geometric sequence
geometric sequence
sequence in which the ratio of consecutive terms is a constant
common ratio
the constant in a geometric sequence ("r)
arithmetic sequence
sequence in which the difference between successive terms is a constant
arithmetic means
the average of two terms in an arithmetic sequence
geometric mean
the terms between two given terms in a geometric sequence
mean proportional
geometric mean
common difference
the constant in an arithmetic sequence
sequence
a function defined on the set of consecutive positive integers or a subset of consecutive positive integers
term
value in a sequence
general term
n-th term
finite sequences
terminates
infinite sequence
never ends
recursive formula
ex: a1= 28
a(n+1)= (an) -4
(need past terms to solve)
explicit formula
ex: a(n)=3(n)
(dont need past terms to solve)
exponental equations
an equation with a variable in the exponent
ex: y= 3^x
hyperbola
set of all points in a plane such that the difference of the distances from P to two fixed points is a constant
ellipse
set of all points in a plane such that the sum of the distances from P to two fixed points is a constant
parabola
set of all points P in a plane that are the same distance from a given line and a fixed point not on a line
circle
set of all points P in a plane that are the same distance (radius) from a given point (center)
rational algebraic function
function that can be represented as the quotient of two polynomials
asymptote
line (axis) the graph approaches but doesn't cross
location theorem
if f(x) is a polynomial function with real coefficients and a and b are real numbers such that f(a) is positive and f(b) is negative then at leaast one zero of f(x) occurs between a and b
upper bound
a number greater than or equal to the greatest real zero of the function
lower bound
a number less than or equal to the least zero of a function
complex conjugate theorem
if a complex number, a + bi, is a solution of a polynomial equation with real coefficients, then the conjugate, a-bi, is also a solution of the equation
rational zero theorem
if a polynomial function has integral coefficients and if it has a rational zero p/q where p and q are relatively prime, the p is a factor of the constant term and the q is a factor of the leading coefficient
remainder theorem
if p(x) is a polynomial and a is a number and if p(x) is divided by x-a then the remainder is p(a)
factor theorem
if p(x) is a polynomial then x-a is a factor of p(x) if and only if p(a)=0
complex number
sum of a real number and a pure imaginary number
radical equation
an equation that has a variable in the radicand
extraneous root
when you check it the answer does not work
perfect square
the product of two equal rational expressions
principal square root
the positive square root