∑ ((-1)^n*x^n)/n! is the Taylor series about zero for what function?

Answer: e^-x

Tutors, sign in to answer this question.

∑ (x^n)/n! = e^x, n from 0 to ∞

∑ ((-1)^n*x^n)/n!, n from 0 to ∞

= ∑ ((-x)^n)/n!, n from 0 to ∞

= e^-x

Taylor Series at x = 0 is the Maclaurin Series.

It says that a function f(x) can be approximated by an infinite series:

f(x) = f(0) + f'(0) * x + f''(0) * x^2/2! + f'''(0) * x^3/3! + ...

If f(x) = e^x then all the derivatives are also e^x and at x = 0 are all 1.

So f(x) = 1 + x + x^2/2! + x^3/3! + ... = sum[n=0 to inf][x^n/n!] = e^x.

f(-x) = 1 - x + x^2/2! - x^3/3! + ... = sum[n=0 to inf][(-1)^n * x^n/n!] = e^(-x).

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Deborah V.

Alg. 1, 2 Geom, Precalc, Chemistry, Teas, SAT, ACT, French, ASVAB, Art

$11.25 per 15 min

View Profile >

Philip P.

Effective and Affordable Math Tutor

$11.25 per 15 min

View Profile >

Milton Rafael N.

Math, ACT, GRE, SAT, ASVAB,TEAS, Engineering, Spanish & more

$8.75 per 15 min

View Profile >

## Comments