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Final Cal Project


1-x+x^2-....+(-x)^n 1/1+x
x-x^3/3!+x^5/5!-....+(-1)^n(x^2n+1)/(2n+1)! sin(x)
1+x+x^2/2!+....+x^n/n! e^x
1+x+x^2+....+x^n 1/1-x
1-x^2/2!+x^4/4!-...+(-1)^n(x^2n)/(2n)! cos(x)
x-x^2/2+x^3/3-....+(-1)^n(x^n)/n ln(1+x)
f(0)+f'(0)x+f"(0)x^2/2!..... (Power)Taylor Series generated by f at x=0
f(a)+f'(a)(x-a)+f"(a)(x-a)^2/2! (Power) Taylor Series generated by f at x=a
Sequence a succession of numbers in order
Series the sum of a sequence
Series in which each term is obtained by adding a constant to the precedin term. Arithmetic series
Series in which each term is obtained by multiplying the preceding term by a constant Geometric series
Series in which the terms alternate between positive and negative Alternating series
1/1+1/2+1/3+1/4+1/5+1/6+1/7.... Harmonic series
Series that has infinitely many terms. Infinite series
the sum of the first n terms of a series. Partial sum
An infinite series that has a limit as n approches infinity. Convergent series
An infinite series that has no limit as n approches infinity. Divergent series
An infinite Geometric series converges to? a/(1-r) when |r|=1
What is an Interval of Convergence? The interval on which the series (polynomial) represents the function. (sum)
What is the Radius of convergence? The radius of convergence is half the length of the interval of convergence.
What is the center of convergence? The midpoint of the interval of convergence.
Does the harmonic series converge or diverge? always diverges.
Where does an Alternating Series converge? Converges if 1) |a1|>|a2|>|a3| or
Created by: Lone_Rider