Taylor for cosx
our series
ahaa what do you think now
The problem says, "Write down the Taylor series of about and sum the series "
First question is, when do you stop writing terms of the series if it doesn't tell you?
Also, what does the second series have to do with the first one? This seems like two totally different problems crammed into one. Am I wrong?
You don't. A Taylor polynomial stops after a finite number of terms. A Taylor series is an infinite series.
The Taylor series for cos(x) isAlso, what does the second series have to do with the first one? This seems like two totally different problems crammed into one. Am I wrong?
The sum you are given is either or since, in what you wrote, it is not clear whether the is supposed to be in the numerator or denominator.
In either case, notice that we have n! in the denominator, as in the cos(x) series. Now, because of the " " in the cos(x) series, try to try powers as "2n". We can write and, of course,
That is, depending upon whether the " is in the numerator or denominator we get
or
.