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