Calc Flashcards Power Series
What is the power series of 1/x?
(-1)^n * (x - 1)^n
What is the power series of 1/(1+x)?
(-1)^n * x^n
What is the power series of ln x?
((-1)^n-1 * (x - 1)^n)/n
What is the power series of e^x?
(x^n)/n!
What is the power series of sin x?
((-1)^n * x^(2n + 1))/(2n + 1)!
What is the power series of cos x?
((-1)^n * x^(2n + 1))/(2n)!
What is the power series of arctan x?
((-1)^n * x^(2n + 1))/(2n + 1)
What is the power series of arcsin x?
((2n)! * x^(2n + 1))/((2^n * n!)^2 * (2n + 1))
What is the power series of (1 + x)^k?
(k(k - 1)(k - 2)(k - 3)x^4)/4!
What is the interval of convergence of 1/x?
0 < x < 2
What is the interval of convergence of 1/(1+x)?
-1 < x < 1
What is the interval of convergence of ln x?
0 < x <= 2
What is the interval of convergence of e^x?
-infinity < x < infinity
What is the interval of convergence of sin x?
-infinity < x < infinity
What is the interval of convergence of cos x?
-infinity < x < infinity
What is the interval of convergence of arctan x?
-1 <= x <= 1
What is the interval of convergence of arcsin x?
-1 <= x <= 1
What is the interval of convergence of (1 + x)^k
-1 < x < 1 (The convergence at x = +/-1 depends on the value of k.)
