Level 633 Level 635
Level 634

Power Series


28 words 0 ignored

Ready to learn       Ready to review

Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

All None

Ignore?
arctan(x)
∑ (-1)^n x^(2n+1)/(2n+1) for |x|≤1
sin(x)
∑ (-1)^n x^(2n+1)/(2n+1)! for all real x
cos(x)
∑ (-1)^n x^(2n)/(2n)! for all real x
1/1-x
∑ x^n for |x|<1
1/1+x
∑ (-1)^n x^n for |x|<1
ln(1+x)
∑(-1)ⁿ⁻¹ xⁿ/n (n=1, ∞)
e^x
∑ x^n/n! for all real x
sinx
x - [(x^3) / 3!] + [(x^5) / 5!] + ... [(x^(2n+1))(-1^n) / (2n + 1)!] [0, infinity)
cosx
1 - [(x^2) / (2!)] + [(x^4) / (4!)] + ... [(-1^n)(x^2n) / (2n)!] [0, infinity)
e^x
1 + x + [(x^2) / 2!] + ... [(x^n) / n!] [0, infinity)
ln(1 + x)
x - [(x^2) / 2] + [(x^3) / 3] + ... [(-1^n)(x^(n + 1)) / (n + 1)] [1, infinity)
1 / (1 - x)
1 + x + x^2 + ... x^n [0, infinity)
lnx
(x - 1) - (1/2)(x - 1)^2 + (1/3)(x - 1)^3 + ... (-1^(n + 1))(1/n)(x - 1)^n [1, infinity)
General Form for a MacLaurin
(f(0) / 0!)(x^0) + (f'(0) / 1!)(x^1) + (f"(0) / 2!)(x^3) + ...
General Form for a Taylor
f(a)(x - a)^0 + [(f'(a)(x - a)^1) / (1!)] + [(f"(a)(x - a)^2) / (2!)] + ...
e^x
xⁿ/n!
sinx
(-1)ⁿ(x)²ⁿ⁺¹/(2n+1)!
cosx
(-1)ⁿ(x)²ⁿ/(2n)!
arctanx
(-1)ⁿ(x)²ⁿ⁺¹/(2n+1)
1/x
(-1)ⁿ(x-1)ⁿ
1/x+1
(-1)ⁿ(x)ⁿ
lnx
(-1)ⁿ⁻¹(x-1)ⁿ/n
1/(1-x)
∑ x^n; |x|<1
1/(1+x)
∑ (-1)^n x^n; |x|<1
ln(1+x)
∑ (-1)^n [x^(n+1)/(n+1)]; -1<x≤1
e^x
∑ (x^n)/n!; |x|<∞
cosx
∑ [(-1)^n x^(2n)]/(2n)!; |x|<∞
sinx
∑ [(-1)^n x^(2n+1)]/(2n+1)!; |x|<∞