Sequences and Series | Exponential and Logarithmic Functions |
Sequence: a function whose domain is a set of integers Series: the sum of sequences Summation Notation: the sum of all terms beginning with i and ending with the nth term Infinite series: a series where the number of terms is infinite Geometric series: each term is obtained from the previous term by multiplying by a constant, r Arithmetic series: a series where the difference between terms is a constant; an arithmetic series will be a straight line P-Series: a sequence in which n is raised to the power of a negative integer, p Alternating Series: a series in which each term alternates between positive and negative Convergence: a sequence converges if it has a limit S as n approaches infinity Divergence: a sequence diverges if it does not have a limit S as n approaches infinity Recursive sequence: a sequence where each term is related to the preceding term by a formula
Ratio Test Let ![]() ![]() Then, the series converges if ![]() ![]() ![]() Limit Comparison Test If ![]() ![]() ![]() If ![]() ![]() ![]() If ![]() ![]() ![]() Direct Comparison Test Let ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Exponential function: a function defined as a constant b raised to the power x; the most common exponential function is the case where b is the special number e. Logarithmic function: a function defined as logb of x where b is the base Natural logarithmic function: a logarithmic function where the base is the number e, written as ![]() ![]() ![]() ![]() ![]() ![]() ![]()
Polar Coordinates: system of coordinates defined by a radius r, and an angle ![]() Complex Number: a number defined as z=x+iy, where x is real component, y is imaginary component and I is defined as ![]()
DeMoivre’s Theorem |
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