Problem 57983. Easy Sequences 109: Summation of Derivatives of a Trigonometric Function

A trigonometric function, , is defined as follows:
where: ; and
x is in radians.
In this problem we are asked to evaluate the following summation:
where: x is a real number;
n is an integer;
or the k-th derivative of T with respect to x; and
.
For example for and , we have:
>> syms x;
>> T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);
>> S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;
>> s = vpa(subs(S,x,2))
s = 0.10315887444431633673347091141408;
Please present the final output rounded-off to 6 decimal places. Therefore the final answer is .
-------------------------
NOTE: Symbolic toolbox is not available to Cody players. It is possible to do numerical differentiation in Matlab without symbolic toolbox. Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using syms, as shown above.
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Solution Stats

62.5% Correct | 37.5% Incorrect
Last Solution submitted on Jun 05, 2023

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