Question

Find the Maclaurin series representation of 2*e^(2x+1) and use it to approximate 2*e^5 to 6 decimal places.

Answer 1

I know that the Maclaurin series for e^x is:
\[\sum_{n=0}^{\infty} \frac{ x^{n} }{ n! }\]
So would this series be:
\[2\sum_{n=0}^{\infty} \frac{ (2x+1)^{n} }{ n! }?\]

Answer 2

yeah i guess you could expand that way
or else just expand

Answer 3

OK.
Though honestly I don't think I need to do anything other than just plug 5 into the original series. XD silly calculus problems.