- #1

ggcheck

- 87

- 0

Find the Maclaurin series for f(x) = (x^2)(e^x)

the book suggests obtaining the Maclaurin series of f(x) by multiplying the known Maclaurin series for e^x by x^2:

(x^2)(e^x) = (x^2)(1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...)

= x^2 + x^3 + (x^4)/2! + (x^5)/3! + (x^6)/4! + ... = sum(from n=2, infin) (x^n)/(n-2)!

my question is:

why can we multiply the Maclaurin series for e^x by x^2? wouldn't we have to multiply one Maclaurin series by another, i.e. the Maclaurin series of e^x by the Maclaurin series for x^2?

I hope this questions makes sense. Thanks

the book suggests obtaining the Maclaurin series of f(x) by multiplying the known Maclaurin series for e^x by x^2:

(x^2)(e^x) = (x^2)(1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...)

= x^2 + x^3 + (x^4)/2! + (x^5)/3! + (x^6)/4! + ... = sum(from n=2, infin) (x^n)/(n-2)!

my question is:

why can we multiply the Maclaurin series for e^x by x^2? wouldn't we have to multiply one Maclaurin series by another, i.e. the Maclaurin series of e^x by the Maclaurin series for x^2?

I hope this questions makes sense. Thanks

Last edited: