How do you solve #sum_(i=1)^5 (-1)^i/(i!)#?

1 Answer
George C.
Feb 7, 2017

#sum_(i=1)^5 ((-1)^i)/(i!) = -19/30#

Explanation:

With this example, it is probably easiest to just expand out and sum the five terms manually:

#sum_(i=1)^5 ((-1)^i)/(i!) = -1/(1!)+1/(2!)-1/(3!)+1/(4!)-1/(5!)#

#color(white)(sum_(i=1)^5 ((-1)^i)/(i!)) = -1+1/2-1/6+1/24-1/120#

#color(white)(sum_(i=1)^5 ((-1)^i)/(i!)) = -1/2-1/6+1/24-1/120#

#color(white)(sum_(i=1)^5 ((-1)^i)/(i!)) = -5/8-1/120#

#color(white)(sum_(i=1)^5 ((-1)^i)/(i!)) = -19/30#

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