The summation from n=0 to inf. of [(-1)^n]/[n!] equals 1/e
2006-07-20 11:18:58 · 4 answers · asked by frostwizrd 2 in Science & Mathematics ➔ Mathematics
Since this is an alternating series that is decreasing, you need to find the term where the absolute value of your term is less than twice the error you are looking for, or in other words:
1/n! < 2*(.001)
n! > 500
So n>= 6
Taking the sum of the first six terms you get a difference of 0.00000168
Taking the sum of the first five terms you get a difference of .00138
2006-07-20 11:24:28 · answer #1 · answered by fatal_flaw_death 3 · 0⤊ 0⤋
You need to use Taylor's Theorem! Estimate the remainder term somehow and find out how many terms you need before your estimate is less than .001
2006-07-20 18:28:00 · answer #2 · answered by Aaron 3 · 0⤊ 0⤋
Try the # 9 it's the magic # in math
2006-07-20 18:23:43 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Very, very carefully...
2006-07-20 18:21:31 · answer #4 · answered by KnowhereMan 6 · 0⤊ 0⤋