11 grade maths others
What is the taylor series expansion for the tangent function left tan x ight?
What is the taylor series expansion for the tangent function left tan x ight?
1 Answer
Askiitians Tutor Team
The Taylor series expansion for the tangent function, centered at 0 (also known as the Maclaurin series), is given by:
tan(x) = x + (x^3)/3 + (2x^5)/15 + (17x^7)/315 + ...
In general, the nth term of the series can be expressed as:
T_n(x) = (-1)^(n-1) * B_(2n) * (2^(2n) - 1) * x^(2n-1) / (2n)!
where n is a positive integer, B_(2n) is the (2n)th Bernoulli number, and n! represents the factorial of n.
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