# Calculus

Approximate the sum of the series correct to four decimal places.
n=1 to infinity
(-1)^n/4^n*n!

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. If you notice that the Taylor's series expansion of
e^(-x/4) =
1-x/4+x^2/32-x^3/384+x^4/6144-...
is exactly the given series less the first term with x=1,
so
the given series is
e^(-1/4)-1 = -0.2212 to four places.

If you sum term by term, you just need to sum until the next term falls below 0.00001, which is around the 5th term.

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

Still need help? You can ask a new question.