Let f be a real-valued function, and suppose ∑ n=0
[infinity]
​
a n
​
x n
is the Maclaurin series for f. The coefficients of the Maclaurin series, a n
​
, depend on the function f. (c) If f(x)=ln(1+x), then the nth coefficient of the Maclaurin series for f is when n≥1, while a 0
​
= In the following, we'll consider some trigonometric functions; notice that many of the coefficients in these Maclaurin series are 0 the Maclaurin series, so take particular care. (d) For example, suppose f(x)=cosx. In this case, the Maclaurin series for f is ∑ n=0
[infinity]
​
b n
​
x 2n
where b n
​
= (e) Finally, if f(x)=sinx, then the Maclaurin series for f is ∑ n=0
[infinity]
​
b n
​
x 2n+1
where b n
​
=